Fix SCCNonlinearProblem not having u0 field (issue #758)

[ChrisRackauckas-Claude]

Summary

• Fix SCCNonlinearProblem solve failing when u0 is not explicitly provided
• SCCNonlinearProblem does not have a u0 field - each subproblem has its own u0
• The solve function was incorrectly trying to access prob.u0, causing a FieldError

Changes

• Remove the u0 = u0 !== nothing ? u0 : prob.u0 fallback since SCCNonlinearProblem has no u0 field
• The u0 parameter is only used for AD hooks, not for actual solving
• Add regression test to prevent this from happening again

Test plan

• Verified fix works locally with the MWE from issue SCCNonlinearProblem has no field u0 in SCCNonlinearSolve 1.7 #758
• Existing "Manual SCC" test still passes
• New regression test added for issue SCCNonlinearProblem has no field u0 in SCCNonlinearSolve 1.7 #758
• Wait for CI to complete

Closes #758

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

Additional Fix: ExplicitImports error on macOS CI

The macOS CI was failing due to an ExplicitImports check error:

Module `SCCNonlinearSolveChainRulesCoreExt` is relying on the following implicit imports:
* `SCCNonlinearSolve` which is exported by `SCCNonlinearSolve`

This was a pre-existing issue in the ChainRulesCore extension that became visible during CI. Fixed by changing:

using SCCNonlinearSolve
using SCCNonlinearSolve: SCCAlg, scc_solve_up

to:

import SCCNonlinearSolve: SCCAlg, scc_solve_up

This avoids the implicit import of the module name itself and satisfies the ExplicitImports check.

All tests now pass locally (26/26).

[ChrisRackauckas-Claude]

Fix: Code formatting

Fixed code formatting in test file to pass CI code-style checks:

• Added spaces around = operators in assignments
• Added spaces around arithmetic operators (+, -, *)

All 26 SCCNonlinearSolve tests pass locally.

[ChrisRackauckas-Claude]

CI Status Summary

Core tests passing:

• ✅ test (1, macos-latest)
• ✅ test (1, ubuntu-latest)
• ✅ test (1.11, macos-latest)
• ✅ test (lts, macos-latest)
• ✅ test (lts, ubuntu-latest)
• ✅ ModelingToolkit.jl tests (Initialization, InterfaceI, InterfaceII)
• ✅ OrdinaryDiffEq.jl tests (Interface, Regression)

Pre-existing CI issues (also failed on merged PR #757):

• Spell Check: Pre-existing typos in NonlinearSolveBaseReverseDiffExt.jl and NonlinearSolveBaseEnzymeExt.jl
• code-style: Pre-existing formatting issues
• downgrade / test: CI infrastructure issue (403 errors in workflow telemetry)

All code changes have been tested locally and pass. The PR is ready for review.