Add downgrade CI for all sublibraries

This adds a comprehensive downgrade CI workflow that tests compatibility
for the main package and all 10 sublibraries in the lib/ directory:

Main package: .
Sublibraries: BracketingNonlinearSolve, NonlinearSolveBase, NonlinearSolveFirstOrder, NonlinearSolveHomotopyContinuation, NonlinearSolveQuasiNewton, NonlinearSolveSciPy, NonlinearSolveSpectralMethods, SCCNonlinearSolve, SciMLJacobianOperators, SimpleNonlinearSolve

Each sublibrary is tested individually with downgraded dependencies
to ensure compatibility across the ecosystem.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: claude

.github/workflows/DowngradeSublibraries.yml

@@ -0,0 +1,48 @@
+name: Downgrade Sublibraries
+on:
+  pull_request:
+    branches:
+      - master
+    paths-ignore:
+      - 'docs/**'
+  push:
+    branches:
+      - master
+    paths-ignore:
+      - 'docs/**'
+jobs:
+  test:
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        downgrade_mode: ['alldeps']
+        julia-version: ['1.10']
+        project:
+          - '.'
+          - 'lib/BracketingNonlinearSolve'
+          - 'lib/NonlinearSolveBase'
+          - 'lib/NonlinearSolveFirstOrder'
+          - 'lib/NonlinearSolveHomotopyContinuation'
+          - 'lib/NonlinearSolveQuasiNewton'
+          - 'lib/NonlinearSolveSciPy'
+          - 'lib/NonlinearSolveSpectralMethods'
+          - 'lib/SCCNonlinearSolve'
+          - 'lib/SciMLJacobianOperators'
+          - 'lib/SimpleNonlinearSolve'
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.julia-version }}
+      - uses: julia-actions/julia-downgrade-compat@v2
+        with:
+          project: ${{ matrix.project }}
+          skip: Pkg,TOML
+      - uses: julia-actions/julia-buildpkg@v1
+        with:
+          project: ${{ matrix.project }}
+      - uses: julia-actions/julia-runtest@v1
+        with:
+          project: ${{ matrix.project }}
+          ALLOW_RERESOLVE: false