Why does `remake` ignore my `u0`?

[bradcarman]

Take the following...

using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using OrdinaryDiffEq
using CairoMakie

pars = @parameters begin
    k(t)
end

vars = @variables begin
    x(t)
end

eqs = [
    D(x) ~ (k - x)
]

@mtkbuild sys = ODESystem(eqs, t, vars, pars)
prob = ODEProblem(sys, [x=>0], (0, Inf), [k => 0])
integrator = init(prob, Rodas5P())

dt=0.1
for i=1:100
    integrator.ps[sys.k] = ((i-1)*dt)^2
    step!(integrator, dt, true)
end

prob_copy = remake(prob; u0=integrator.u, p = integrator.p, tspan= (99*dt, Inf))
integrator_copy = init(prob_copy, Rodas5P(); initializealg=CheckInit())

for i=101:200
    integrator.ps[sys.k] = ((i-1)*dt)^2
    integrator_copy.ps[sys.k] = ((i-1)*dt)^2
    step!(integrator, dt, true)
    step!(integrator_copy, dt, true)
end

time = 0:dt:199*dt
time_copy = 10:dt:199*dt

fig = Figure()
ax = Axis(fig[1,1], xlabel="time [s]", ylabel="sys.x")
lines!(ax, time, integrator.sol(time; idxs=sys.x).u; label="integrator")
scatter!(ax, time_copy, integrator_copy.sol(time_copy; idxs=sys.x).u; color=:red, label="integrator_copy")
axislegend(ax; position=:lt)
fig

This gives the following...

If I transfer the state u0 and the parameters p from integrator to integrator_copy, why does integrator_copy start at 0 instead of 81?

using ModelingToolkit v9.79.0