refactor: update to new SciMLBase remake API hooks with context structs#4496
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SciMLBase v3.1.0 (commit 09770ffa, 2026-04-10, "refactor: pass context struct to late_binding_update_u0_p") added a trailing `ctx::LateBindingUpdateU0PContext` argument (with default) that the v3 public path now forwards as an 8th positional. MTK's 7-arg overload no longer dispatches; SciMLBase's 8-arg no-op fallback wins, so `newp.initials` was never updated and `initialize_dae!` then re-solved `u` against the stale `Initial` values. This surfaced as four failing assertions in the OrdinaryDiffEq.jl `reinit! updates initial parameters` testset (lib/OrdinaryDiffEqNonlinearSolve/test/modelingtoolkit/dae_initialize_integration.jl:98-101). Wraps the original body in a small `_late_binding_update_u0_p_impl` helper and dispatches via `@static if isdefined(SciMLBase, :LateBindingUpdateU0PContext)` so the patch keeps working on the SciMLBase v2 line that the package's `[compat]` still supports (`SciMLBase = "2.149.0, 3"`). On v3.1.0+ the 8-arg method matches; on v2 the 7-arg method is defined as before. Verified locally: with this patch and SciMLBase v3.6.0 resolved, the OrdinaryDiffEq `reinit! updates initial parameters` testset goes from 4 fail / 4 pass to 8 / 8 pass. Fixes #4473. Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
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Supersedes #4474