Add SparseConnectivityTracer test compat

[ChrisRackauckas-Claude]

Ignore this PR until it has been reviewed by @ChrisRackauckas.

Summary

• add a SparseConnectivityTracer = "1" compat bound for the matrix-free NonlinearSolveAlg test dependency
• bump OrdinaryDiffEqNonlinearSolve from 2.3.0 to 2.3.1

Root cause

Commit 9a2f7e7b7 added SparseConnectivityTracer to test extras for TracerSparsityDetector() but omitted its compat entry. Aqua therefore fails the OrdinaryDiffEqNonlinearSolve QA lane. The 1.x bound targets the stable API series containing the exported ADTypes sparsity detector used by the test.

Validation

• Aqua.test_deps_compat(OrdinaryDiffEqNonlinearSolve) on Julia 1.11: passed 4/4, including the extras check
• exact ODEDIFFEQ_TEST_GROUP=QA julia +1.11 --project=lib/OrdinaryDiffEqNonlinearSolve -e "using Pkg; Pkg.test()": compat bounds passed 4/4; the run remains red only on the 11 pre-existing cross-sublibrary public-API errors tracked in ExplicitImports: drive sublibrary QA checks to green (ei_broken markers) #3776
• julia +1.12 -m Runic --check --diff --verbose .: all 1000 Julia files passed

This PR does not add an ExplicitImports allowance or otherwise silence #3776.

[ChrisRackauckas-Claude]

Four-hour CI checkpoint

The scheduled timer expired at 2026-07-16 22:00:07 EDT; this snapshot was collected immediately afterward.

Branch / PR state

• Fetched both upstream and origin: the branch is 0 commits behind upstream/master and 1 commit ahead.
• The worktree is clean and matches origin/agent/sct-test-compat.
• PR remains a draft, GitHub reports it MERGEABLE, and mergeStateStatus is UNSTABLE because of the classified failing checks below.
• Full rollup: 170 checks — 146 successful, 20 failed, 3 skipped, 1 queued.
• The only incomplete check is StochasticDiffEq NoncommutativeConvergence, still queued with no runner assigned.

Patch-relevant OrdinaryDiffEqNonlinearSolve lanes

• Core: Julia LTS passed, Julia current passed, and Julia pre passed.
• ModelingToolkit passed.
• QA failed, but its Aqua dependency-compatibility section passed 4/4 and the log resolved/precompiled SparseConnectivityTracer v1.2.2. Its only residual failure is the same 11-name public-boundary check tracked by #3776.
• Downgrade failed after successfully resolving SparseConnectivityTracer v1.2.2; its residual is the pre-existing NonlinearSolveBase v2.33.0 / similar(::SciMLOperators.MatrixOperator) error in linear_nonlinear_tests.jl (36 passed, 1 errored). This matches the master regression introduced with NonlinearSolveAlg: reuse the ODE WOperator matrix-free for Krylov linsolves #3885; the upstream fix path is NonlinearSolve.jl #1089.

Remaining failures

The 20 completed failures classify into existing master failure buckets:

• 8 downgrade jobs: the NonlinearSolveAlg: reuse the ODE WOperator matrix-free for Krylov linsolves #3885 compatibility-floor regression.
• 10 QA jobs: the public-boundary architecture tracked by ExplicitImports: drive sublibrary QA checks to green (ei_broken markers) #3776.
• 1 BDF Core job: the same NonlinearSolveAlg: reuse the ODE WOperator matrix-free for Krylov linsolves #3885 / NonlinearSolve.jl lddrk25 #1089 path.
• 1 GPU job: the exact master signature (24 passed, 137 failed, 11 broken), tracked by #3922, #3923, and upstream CUDA.jl #3199.

No completed failure attributable to this SCT compatibility-only patch was found.

Local verification

• Focused Aqua.test_deps_compat(OrdinaryDiffEqNonlinearSolve) passed all four dependency sections.
• The exact full QA run confirms that compat now passes and retains only the ExplicitImports: drive sublibrary QA checks to green (ei_broken markers) #3776 public-boundary failure; it is not reported as fully green.
• Runic completed successfully over all 1,000 Julia files.