Bump SciMLBase compat to v3 and RecursiveArrayTools to v4

[ChrisRackauckas-Claude]

Summary

• Bumps SciMLBase compat bounds to include v3 across all 12 subpackages (root, docs, BracketingNonlinearSolve, NonlinearSolveBase, NonlinearSolveFirstOrder, NonlinearSolveHomotopyContinuation, NonlinearSolveQuasiNewton, NonlinearSolveSciPy, NonlinearSolveSpectralMethods, SCCNonlinearSolve, SciMLJacobianOperators, SimpleNonlinearSolve, test/trim)
• Bumps RecursiveArrayTools compat in NonlinearSolveBase to include v4 (required by SciMLBase v3)
• Supersedes CompatHelper PRs CompatHelper: bump compat for SciMLBase to 3, (keep existing compat) #897-CompatHelper: bump compat for SciMLBase to 3 for package SimpleNonlinearSolve, (keep existing compat) #908 and CompatHelper: bump compat for RecursiveArrayTools to 4 for package NonlinearSolveBase, (keep existing compat) #887

Breaking changes audit

Verified that NonlinearSolve does not use any APIs removed in SciMLBase v3:

Removed API	Used in NonlinearSolve?
u_modified! (→ derivative_discontinuity!)	No
Type aliases DEAlgorithm, DEProblem, DESolution, SciMLSolution	No
AbstractDEAlgorithm (still exists in v3, only short aliases removed)	Used ✓ safe
Deprecated solution accessors .destats, .minimizer, .minimum, .prob	.minimizer used only on LeastSquaresOptim/SpeedMapping results, not SciMLBase solutions. .prob used on NonlinearSolve's own cache types.
symbol_to_ReturnCode, sys_or_symbolcache	No
Old iterators tuples(), intervals()	No
Solution AbstractArray indexing changes	ODE solution in tests uses callable interpolation sol(t)[i], not direct indexing
nout/batch kwargs, syms/paramsyms/indepsym kwargs	No

No code changes required — only compat bound updates.

Test plan

• CI passes with existing SciMLBase v2.x (compat allows both v2 and v3)
• Once upstream deps (LinearSolve, LineSearch, etc.) also bump, SciMLBase v3 will resolve and CI should pass

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