Type promotion issue with `SCCNonlinearProblem` in initialization

**Describe the bug 🐞**

I'm trying to setup an optimization over a DAE solve that has a `SCCNonlinearProblem` in initialization and it's fully determined, but I'm getting a `Float64(::ForwardDiff.Dual...)` error from initialization.

For some reason, it seems that `u0` is not promoted when using `SII.setsym_oop`. I'm not sure if that's expected or I'm missing something.

**Expected behavior**

No errors.

**Minimal Reproducible Example 👇**

Without MRE, we would only be able to help you to a limited extent, and attention to the issue would be limited. to know more about MRE refer to [wikipedia](https://en.wikipedia.org/wiki/Minimal_reproducible_example) and [stackoverflow](https://stackoverflow.com/help/minimal-reproducible-example).

```julia
using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using OrdinaryDiffEqRosenbrock, OrdinaryDiffEqNonlinearSolve
using SymbolicIndexingInterface
using SciMLBase
using DifferentiationInterface

function build_model(; name)
    @parameters g l = 1
    @variables x(t) [state_priority = 10] y(t) λ(t)
    eqs = [D(D(x)) ~ λ * x
        D(D(y)) ~ λ * y - g
        x^2 + y^2 ~ l^2]
    ODESystem(eqs, t; name)
end

pend = structural_simplify(build_model(name=:pend))

@unpack x, y, g, λ = pend

prob = ODEProblem(pend, [x => √2 / 2, D(x) => √2 / 2], (0.0, 0.5), [g => 1.], guesses=[λ => 1, y => √2 / 2])

sol = solve(prob, Rodas5P())
# plot(sol, idxs = (x,y), aspect_ratio=1)

data = sol(0:0.1:0.5, idxs=x + y).u

setter = setsym_oop(prob, [g]);

get_vars = getsym(prob, [pend.x + pend.y]);

function loss(x, (prob, ts, setter, get_vars, data))
    (u0, p) = setter(prob, x)

    new_prob = remake(prob; u0, p)
    new_sol = solve(new_prob, Rodas5P(); saveat=ts)

    u = get_vars(new_sol)

    SciMLBase.successful_retcode(new_sol) && return Inf

    sum(abs.(reduce(vcat, u) - data)) / length(u)
end

prob0_f = ODEProblem(pend, [x => √2 / 2, D(x) => √2 / 2], (0.0, 0.5), [g => 0.7], guesses=[λ => 1, y => √2 / 2]) # fully determined

ts = collect(0:0.1:0.5)
ps = (prob0_f, ts, setter, get_vars, data);

x0 = [1.3]

DifferentiationInterface.gradient(x -> loss(x, ps), AutoForwardDiff(), x0)
```

**Error & Stacktrace ⚠️**

```julia
ERROR: MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{var"#12#13", Float64}, Float64, 1})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  (::Type{T})(::Real, ::RoundingMode) where T<:AbstractFloat
   @ Base rounding.jl:265
  (::Type{T})(::T) where T<:Number
   @ Core boot.jl:900
  Float64(::IrrationalConstants.Invπ)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/lWTip/src/macro.jl:131
  ...

Stacktrace:
  [1] convert(::Type{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{var"#12#13", Float64}, Float64, 1})
    @ Base ./number.jl:7
  [2] setindex!(A::Vector{Float64}, x::ForwardDiff.Dual{ForwardDiff.Tag{var"#12#13", Float64}, Float64, 1}, i::Int64)
    @ Base ./array.jl:987
  [3] macro expansion
    @ ~/.julia/packages/SymbolicUtils/0GKgW/src/code.jl:460 [inlined]
  [4] macro expansion
    @ ~/.julia/packages/Symbolics/kQzvO/src/build_function.jl:137 [inlined]
  [5] macro expansion
    @ ~/.julia/packages/RuntimeGeneratedFunctions/RrXEW/src/RuntimeGeneratedFunctions.jl:161 [inlined]
  [6] macro expansion
    @ ./none:0 [inlined]
  [7] generated_callfunc
    @ ./none:0 [inlined]
  [8] (::RuntimeGeneratedFunctions.RuntimeGeneratedFunction{…})(::Tuple{…}, ::Vector{…}, ::MTKParameters{…})
    @ RuntimeGeneratedFunctions ~/.julia/packages/RuntimeGeneratedFunctions/RrXEW/src/RuntimeGeneratedFunctions.jl:148
  [9] macro expansion
    @ ~/.julia/packages/ModelingToolkit/q2akl/src/systems/codegen_utils.jl:0 [inlined]
 [10] _generated_call(::ModelingToolkit.GeneratedFunctionWrapper{…}, ::Tuple{…}, ::Vector{…}, ::MTKParameters{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/q2akl/src/systems/codegen_utils.jl:262
 [11] (::ModelingToolkit.GeneratedFunctionWrapper{…})(::Tuple{…}, ::Vararg{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/q2akl/src/systems/codegen_utils.jl:259
 [12] (::ModelingToolkit.CacheWriter{…})(p::MTKParameters{…}, sols::Vector{…})
    @ ModelingToolkit ~/.julia/packages/ModelingToolkit/q2akl/src/systems/nonlinear/nonlinearsystem.jl:611
 [13] solve(prob::SCCNonlinearProblem{…}, alg::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}; kwargs::@Kwargs{…})
    @ SCCNonlinearSolve ~/.julia/packages/SCCNonlinearSolve/zfFFF/src/SCCNonlinearSolve.jl:21
 [14] get_initial_values(prob::ODEProblem{…}, valp::OrdinaryDiffEqCore.ODEIntegrator{…}, f::Function, alg::SciMLBase.OverrideInit{…}, iip::Val{…}; nlsolve_alg::NonlinearSolveBase.NonlinearSolvePolyAlgorithm{…}, abstol::Float64, reltol::Float64, kwargs::@Kwargs{})
    @ SciMLBase ~/.julia/packages/SciMLBase/JKXkh/src/initialization.jl:284
 [15] get_initial_values
    @ ~/.julia/packages/SciMLBase/JKXkh/src/initialization.jl:242 [inlined]
 [16] _initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…}, prob::ODEProblem{…}, alg::SciMLBase.OverrideInit{…}, isinplace::Val{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/initialize_dae.jl:151
 [17] _initialize_dae!
    @ ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/initialize_dae.jl:50 [inlined]
 [18] initialize_dae!
    @ ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/initialize_dae.jl:40 [inlined]
 [19] initialize_dae!(integrator::OrdinaryDiffEqCore.ODEIntegrator{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/initialize_dae.jl:40
 [20] __init(prob::ODEProblem{…}, alg::Rodas5P{…}, timeseries_init::Tuple{}, ts_init::Tuple{}, ks_init::Tuple{}, recompile::Type{…}; saveat::Vector{…}, tstops::Tuple{}, d_discontinuities::Tuple{}, save_idxs::Nothing, save_everystep::Bool, save_on::Bool, save_start::Bool, save_end::Nothing, callback::Nothing, dense::Bool, calck::Bool, dt::Float64, dtmin::Float64, dtmax::Float64, force_dtmin::Bool, adaptive::Bool, gamma::Rational{…}, abstol::Nothing, reltol::Nothing, qmin::Rational{…}, qmax::Int64, qsteady_min::Int64, qsteady_max::Rational{…}, beta1::Nothing, beta2::Nothing, qoldinit::Rational{…}, controller::Nothing, fullnormalize::Bool, failfactor::Int64, maxiters::Int64, internalnorm::typeof(DiffEqBase.ODE_DEFAULT_NORM), internalopnorm::typeof(LinearAlgebra.opnorm), isoutofdomain::typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), unstable_check::typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), verbose::Bool, timeseries_errors::Bool, dense_errors::Bool, advance_to_tstop::Bool, stop_at_next_tstop::Bool, initialize_save::Bool, progress::Bool, progress_steps::Int64, progress_name::String, progress_message::typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), progress_id::Symbol, userdata::Nothing, allow_extrapolation::Bool, initialize_integrator::Bool, alias::ODEAliasSpecifier, initializealg::OrdinaryDiffEqCore.DefaultInit, kwargs::@Kwargs{})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/solve.jl:565
 [21] __init (repeats 5 times)
    @ ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/solve.jl:11 [inlined]
 [22] __solve(::ODEProblem{…}, ::Rodas5P{…}; kwargs::@Kwargs{…})
    @ OrdinaryDiffEqCore ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/solve.jl:6
 [23] __solve
    @ ~/.julia/packages/OrdinaryDiffEqCore/LG1u6/src/solve.jl:1 [inlined]
 [24] #solve_call#36
    @ ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:667 [inlined]
 [25] solve_up(prob::ODEProblem{…}, sensealg::Nothing, u0::Vector{…}, p::MTKParameters{…}, args::Rodas5P{…}; kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:1199
 [26] solve_up
    @ ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:1177 [inlined]
 [27] solve(prob::ODEProblem{…}, args::Rodas5P{…}; sensealg::Nothing, u0::Nothing, p::Nothing, wrap::Val{…}, kwargs::@Kwargs{…})
    @ DiffEqBase ~/.julia/packages/DiffEqBase/3HGYN/src/solve.jl:1089
 [28] loss(x::Vector{…}, ::Tuple{…})
    @ Main ~/juliasim/dev/dae_ad.jl:36
 [29] (::var"#12#13")(x::Vector{ForwardDiff.Dual{ForwardDiff.Tag{var"#12#13", Float64}, Float64, 1}})
    @ Main ~/juliasim/dev/dae_ad.jl:54
 [30] vector_mode_dual_eval!
    @ ~/.julia/packages/ForwardDiff/UBbGT/src/apiutils.jl:24 [inlined]
 [31] vector_mode_gradient(f::var"#12#13", x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:91
 [32] gradient
    @ ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:20 [inlined]
 [33] gradient(f::var"#12#13", x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{…}, Float64, 1, Vector{…}})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:17
 [34] gradient(f::var"#12#13", x::Vector{Float64})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/UBbGT/src/gradient.jl:17
 [35] gradient(::var"#12#13", ::AutoForwardDiff{nothing, Nothing}, ::Vector{Float64})
    @ DifferentiationInterfaceForwardDiffExt ~/.julia/packages/DifferentiationInterface/zJHX8/ext/DifferentiationInterfaceForwardDiffExt/onearg.jl:350
 [36] top-level scope
    @ ~/dev/dae_ad.jl:54
Some type information was truncated. Use `show(err)` to see complete types.
```

**Environment (please complete the following information):**

  - Output of `using Pkg; Pkg.status()`

```julia
(jl_34F6Lt) pkg> st
Status `/tmp/jl_34F6Lt/Project.toml`
⌅ [a0c0ee7d] DifferentiationInterface v0.6.54
  [961ee093] ModelingToolkit v9.79.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.8.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.10.0
  [0bca4576] SciMLBase v2.89.1
  [2efcf032] SymbolicIndexingInterface v0.3.40
```

  - Output of `using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)`

```julia
(jl_34F6Lt) pkg> st -m
Status `/tmp/jl_34F6Lt/Manifest.toml`
  [47edcb42] ADTypes v1.14.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [66dad0bd] AliasTables v1.1.3
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.19.0
  [4c555306] ArrayLayouts v1.11.1
  [e2ed5e7c] Bijections v0.1.10
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.6.3
  [70df07ce] BracketingNonlinearSolve v1.2.0
  [2a0fbf3d] CPUSummary v0.2.6
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [861a8166] Combinatorics v1.0.3
  [a80b9123] CommonMark v0.9.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.8
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.173.0
  [459566f4] DiffEqCallbacks v4.5.0
  [77a26b50] DiffEqNoiseProcess v5.24.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
⌅ [a0c0ee7d] DifferentiationInterface v0.6.54
  [8d63f2c5] DispatchDoctor v0.4.19
  [31c24e10] Distributions v0.25.120
  [ffbed154] DocStringExtensions v0.9.4
  [5b8099bc] DomainSets v0.7.15
  [7c1d4256] DynamicPolynomials v0.6.1
  [06fc5a27] DynamicQuantities v1.8.0
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.8
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.1.2
  [1a297f60] FillArrays v1.13.0
  [64ca27bc] FindFirstFunctions v1.4.1
  [6a86dc24] FiniteDiff v2.27.0
  [1fa38f19] Format v1.3.7
⌅ [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [46192b85] GPUArraysCore v0.2.0
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.12.1
  [34004b35] HypergeometricFunctions v0.3.28
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.2
  [8197267c] IntervalSets v0.7.11
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.0
  [ae98c720] Jieko v0.2.1
  [98e50ef6] JuliaFormatter v2.1.2
⌅ [70703baa] JuliaSyntax v0.4.10
  [ccbc3e58] JumpProcesses v9.14.3
  [ba0b0d4f] Krylov v0.10.1
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.7
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.1
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [7ed4a6bd] LinearSolve v3.12.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.16
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [961ee093] ModelingToolkit v9.79.0
  [2e0e35c7] Moshi v0.3.5
  [46d2c3a1] MuladdMacro v0.2.4
  [102ac46a] MultivariatePolynomials v0.5.9
  [d8a4904e] MutableArithmetics v1.6.4
  [d41bc354] NLSolversBase v7.9.1
  [77ba4419] NaNMath v1.1.3
  [8913a72c] NonlinearSolve v4.8.0
  [be0214bd] NonlinearSolveBase v1.9.0
  [5959db7a] NonlinearSolveFirstOrder v1.5.0
  [9a2c21bd] NonlinearSolveQuasiNewton v1.5.0
  [26075421] NonlinearSolveSpectralMethods v1.2.0
  [6fe1bfb0] OffsetArrays v1.17.0
  [429524aa] Optim v1.12.0
  [bac558e1] OrderedCollections v1.8.0
  [bbf590c4] OrdinaryDiffEqCore v1.25.0
  [4302a76b] OrdinaryDiffEqDifferentiation v1.8.0
  [127b3ac7] OrdinaryDiffEqNonlinearSolve v1.8.0
  [43230ef6] OrdinaryDiffEqRosenbrock v1.10.0
  [90014a1f] PDMats v0.11.35
  [d96e819e] Parameters v0.12.3
  [e409e4f3] PoissonRandom v0.4.4
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.27
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.4.0
  [27ebfcd6] Primes v0.5.7
  [43287f4e] PtrArrays v1.3.0
  [1fd47b50] QuadGK v2.11.2
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.6.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.33.0
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.1.1
  [79098fc4] Rmath v0.8.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.14
  [9dfe8606] SCCNonlinearSolve v1.2.0
  [94e857df] SIMDTypes v0.1.0
  [0bca4576] SciMLBase v2.89.1
  [19f34311] SciMLJacobianOperators v0.1.5
  [c0aeaf25] SciMLOperators v0.4.0
  [53ae85a6] SciMLStructures v1.7.0
  [efcf1570] Setfield v1.1.2
  [727e6d20] SimpleNonlinearSolve v2.5.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [a2af1166] SortingAlgorithms v1.2.1
  [0a514795] SparseMatrixColorings v0.4.19
  [276daf66] SpecialFunctions v2.5.1
  [aedffcd0] Static v1.2.0
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.13
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.5
  [4c63d2b9] StatsFuns v1.5.0
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.1
  [2efcf032] SymbolicIndexingInterface v0.3.40
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.27.0
  [0c5d862f] Symbolics v6.39.1
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [ed4db957] TaskLocalValues v0.1.2
  [8ea1fca8] TermInterface v2.0.0
  [1c621080] TestItems v1.0.0
  [8290d209] ThreadingUtilities v0.5.3
  [a759f4b9] TimerOutputs v0.5.28
  [410a4b4d] Tricks v0.1.10
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.2
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.22.1
  [a7c27f48] Unityper v0.1.6
  [897b6980] WeakValueDicts v0.1.0
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [856f044c] MKL_jll v2025.0.1+1
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [f50d1b31] Rmath_jll v0.5.1+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2
```

  - Output of `versioninfo()`

```julia
julia> versioninfo()
Julia Version 1.11.5
Commit 2d89891cf85 (2025-04-22 21:22 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 × Intel(R) Core(TM) i9-14900K
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 32 default, 0 interactive, 16 GC (on 32 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1
```

**Additional context**

I was trying to get a simpler MWE for #3634 and I stumbled over this one 😅 


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Type promotion issue with `SCCNonlinearProblem` in initialization #3635

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Uh oh!

Type promotion issue with SCCNonlinearProblem in initialization #3635

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Type promotion issue with `SCCNonlinearProblem` in initialization #3635