Accept ctx arg in late_binding_update_u0_p for SciMLBase v3.1.0+

[ChrisRackauckas-Claude]

Summary

SciMLBase v3.1.0 (commit 09770ffa, 2026-04-10, refactor: pass context struct to late_binding_update_u0_p) added a trailing ctx::SciMLBase.LateBindingUpdateU0PContext argument to late_binding_update_u0_p. The 6-arg public entry point now forwards ctx as an 8th positional argument internally.

MTK's existing 7-arg overload no longer dispatches against the new 8-arg call site, so SciMLBase's default 8-arg fallback (return newu0, newp) wins and silently drops the Initial(x) parameter propagation in reinit! (and any other call path that goes through late_binding_update_u0_p).

which(...) evidence on the regression:

julia> which(SciMLBase.late_binding_update_u0_p, Tuple{ODEProblem, AbstractSystem, Vector{Pair}, Missing, Float64, Vector{Float64}, MTKParameters, SciMLBase.LateBindingUpdateU0PContext})
late_binding_update_u0_p(prob, sys, u0, p, t0, newu0, newp, ctx::SciMLBase.LateBindingUpdateU0PContext) in SciMLBase   # generic fallback

This PR adds the optional ctx argument to MTK's overload, restoring dispatch under SciMLBase v3.1.0+. The function body is unchanged; this is a 3-line signature update in lib/ModelingToolkitBase/src/systems/nonlinear/initializesystem.jl (lines 686-689).

function SciMLBase.late_binding_update_u0_p(
        prob, sys::AbstractSystem, u0, p, t0, newu0, newp,
        ctx::SciMLBase.LateBindingUpdateU0PContext = SciMLBase.LateBindingUpdateU0PContext()
    )

Fixes #4473.

Unblocks SciML/OrdinaryDiffEq.jl#3553 (which marks the now-fixed reinit! assertions @test_broken until this lands).

Test plan

• Run Runic on the touched file (fredrikekre/runic-action@v1, version 1, matches .github/workflows/FormatCheck.yml). No formatting changes beyond the patch itself.

• Verified locally with the OrdinaryDiffEq.jl NLS_MTK testset: lib/OrdinaryDiffEqNonlinearSolve/test/modelingtoolkit/dae_initialize_integration.jl, testset `reinit!` updates initial parameters (the same one referenced by issue reinit!(integ, new_u0) doesn't update Initial parameters or integ[x] for mtkcompile'd ODE #4473). With the patched MTK developed into the test env (using SciMLBase v3.6.0 from the resolved Manifest):

  Test Summary:                        | Pass  Total  Time
  `reinit!` updates initial parameters |    8      8  4.0s
  

  All 8 assertions pass — both the pre-reinit! checks and the 4 post-reinit! checks (integ.ps[Initial(x)], integ.ps[Initial(y)], integ[x], integ[y]) that the issue identifies as failing.

• CI on this PR (Tests / Downstream / FormatCheck).

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