Merge tri assembly mesh generators and fix detailed mesh regressions

  Unify the triangular subchannel/pin mesh generators behind
  SCMTriAssemblyMeshGenerator and SCMDetailedTriAssemblyMeshGenerator,
  matching the earlier quad-generator merge and the new convention that
  assembly generators build both subchannel and pin meshes when pins
  exist.

  This updates triangular inputs, tests, and registrations to use the new
  assembly generator names directly and removes the old tri alias
  registrations for consistency with the quad side.

  While validating the merged detailed-tri path, fix several regressions:
  - stop mutating TriSubChannelMesh from the detailed visualization generator
  - avoid post-build renumbering in the detailed-tri assembly path
  - copy _pin_nodes in TriSubChannelMesh copy construction
  - assign unique element IDs to generated pin prisms by starting from
    mesh_base->n_elem()

  Also refresh the detailed triangular mesh test baseline to reflect the
  new combined subchannel+pin mesh output and quiet its verbose debug
  logging. Refs #32796

Author: kyriv1980

modules/subchannel/doc/content/modules/subchannel/v&v/ornl_19_pin.md

@@ -66,7 +66,7 @@ The general parameters on the experimental conditions are described here. The pu
 
 ### Mesh
 
-The meshing in SCM uses a custom *SCMTriSubChannelMeshGenerator*.
+The meshing in SCM uses a custom *SCMTriAssemblyMeshGenerator*.
 This one generates a mesh of 1D channel segments connected in 3D.
 The subchannel positions are automatically generated by specifying the number of radial rings, the flat to flat distance of the duct, and the pin pitch.
 The number of axial cells in which the domain is discretrized is specified by *n_cells*.
@@ -121,7 +121,7 @@ A custom transfer, *SCMSolutionTransfer*, is used for this purpose.
 
 !listing /validation/ORNL_19_pin/test_ORNL_19.i block=Transfers language=moose
 
-The detailed mesh uses a *SCMDetailedTriSubChannelMeshGenerator* and the solution variables are populated by the transfer.
+The detailed mesh uses a *SCMDetailedTriAssemblyMeshGenerator* and the solution variables are populated by the transfer.
 
 !listing /validation/ORNL_19_pin/test_ORNL_19.i language=moose
 

modules/subchannel/doc/content/modules/subchannel/v&v/toshiba_37_pin.md

@@ -65,7 +65,7 @@ P_out = 2.0e5 # Pa
 
 ### Mesh
 
-The meshing in SCM uses a custom [SCMTriSubChannelMeshGenerator](source/meshgenerators/SCMTriSubChannelMeshGenerator.md).
+The meshing in SCM uses a custom [SCMTriAssemblyMeshGenerator](source/meshgenerators/SCMTriAssemblyMeshGenerator.md).
 This one generates a mesh of 1D channel segments connected in 3D.
 The subchannel positions are automatically generated by specifying the number of radial rings, the flat to flat distance of the duct, and the pin pitch. The number of axial cells in which the domain is discretrized is specified by *n_cells*.
 For more information about the mesh generator, pelase consult the website documentation on SCM.
@@ -121,7 +121,7 @@ A custom transfer, *MultiAppDetailedSolutionTransfer*, is used for this purpose.
 
 !listing /validation/Toshiba_37_pin/toshiba_37_pin.i block=Transfers language=moose
 
-The detailed mesh uses a *SCMDetailedTriSubChannelMeshGenerator* and the solution variables are populated by the transfer.
+The detailed mesh uses a *SCMDetailedTriAssemblyMeshGenerator* and the solution variables are populated by the transfer.
 
 !listing /validation/Toshiba_37_pin/toshiba_37_pin.i block=viz language=moose
 

modules/subchannel/doc/content/source/meshgenerators/SCMDetailedTriAssemblyMeshGenerator.md

@@ -0,0 +1,17 @@
+# SCMDetailedTriAssemblyMeshGenerator
+
+!syntax description /Mesh/SCMDetailedTriAssemblyMeshGenerator
+
+## Overview
+
+!! Intentional comment to provide extra spacing
+
+This mesh generator creates one detailed 3D visualization mesh containing both the subchannel
+volume and the fuel pin volume for a triangular lattice arrangement. The generated subdomains are
+named `subchannel` and `fuel_pins`.
+
+!syntax parameters /Mesh/SCMDetailedTriAssemblyMeshGenerator
+
+!syntax inputs /Mesh/SCMDetailedTriAssemblyMeshGenerator
+
+!syntax children /Mesh/SCMDetailedTriAssemblyMeshGenerator

modules/subchannel/doc/content/source/meshgenerators/SCMDetailedTriPinMeshGenerator.md

@@ -0,0 +1,21 @@
+# SCMTriAssemblyMeshGenerator
+
+!syntax description /Mesh/SCMTriAssemblyMeshGenerator
+
+## Overview
+
+!! Intentional comment to provide extra spacing
+
+This mesh generator creates the 1D subchannel and pin meshes for a triangular lattice arrangement.
+The generated subdomains are named `subchannel` and `fuel_pins`.
+The center of the mesh is the origin.
+
+## Example Input File Syntax
+
+!listing /test/tests/problems/SFR/sodium-19pin/test19_monolithic.i block=TriSubChannelMesh language=moose
+
+!syntax parameters /Mesh/SCMTriAssemblyMeshGenerator
+
+!syntax inputs /Mesh/SCMTriAssemblyMeshGenerator
+
+!syntax children /Mesh/SCMTriAssemblyMeshGenerator

modules/subchannel/doc/content/source/meshgenerators/SCMDetailedTriSubChannelMeshGenerator.md

@@ -2,7 +2,7 @@
 
 !syntax description /Positions/SCMPinPositions
 
-This object currently requires using a `SubChannel` pin mesh, such as the meshes generated by the [SCMTriPinMeshGenerator.md]
+This object currently requires using a `SubChannel` pin mesh, such as the meshes generated by the [SCMTriAssemblyMeshGenerator.md]
 or the [SCMQuadAssemblyMeshGenerator.md].
 
 !alert note

modules/subchannel/doc/content/source/meshgenerators/SCMTriAssemblyMeshGenerator.md

@@ -29,7 +29,7 @@ n_cells = 100
 
 [Mesh]
   [subchannel]
-    type = SCMDetailedTriSubChannelMeshGenerator
+    type = SCMDetailedTriAssemblyMeshGenerator
     nrings = '${fparse n_rings}'
     n_cells = ${n_cells}
     flat_to_flat = '${fparse duct_inside}'
@@ -40,17 +40,6 @@ n_cells = 100
     pitch = '${fparse fuel_pin_pitch}'
   []
 
-  [fuel_pins]
-    type = SCMDetailedTriPinMeshGenerator
-    input = subchannel
-    nrings = '${fparse n_rings}'
-    n_cells = ${n_cells}
-    unheated_length_entry = '${fparse length_entry_fuel}'
-    heated_length = '${fparse length_heated_fuel}'
-    unheated_length_exit = '${fparse length_outlet_fuel}'
-    pitch = '${fparse fuel_pin_pitch}'
-    pin_diameter = '${fparse fuel_pin_diameter}'
-  []
 []
 
 [AuxVariables]