Add SparseArrays dependency for NonlinearSolvePETScExt

The PETSc extension uses SparseArrays.AbstractSparseMatrix but was missing
SparseArrays from its extension dependencies. This fixes:

- Add SparseArrays to NonlinearSolvePETScExt extension dependencies
- Add SparseArrays back to [weakdeps] (needed by PETSc extension)
- Add SparseArrays compat entry

All other extensions checked and have correct dependencies.

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

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

Author: ChrisRackauckas

Project.toml

@@ -41,6 +41,7 @@ NLSolvers = "337daf1e-9722-11e9-073e-8b9effe078ba"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
 PETSc = "ace2c81b-2b5f-4b1e-a30d-d662738edfe0"
 SIAMFANLEquations = "084e46ad-d928-497d-ad5e-07fa361a48c4"
+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SpeedMapping = "f1835b91-879b-4a3f-a438-e4baacf14412"
 Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
 
@@ -51,7 +52,7 @@ NonlinearSolveLeastSquaresOptimExt = "LeastSquaresOptim"
 NonlinearSolveMINPACKExt = "MINPACK"
 NonlinearSolveNLSolversExt = "NLSolvers"
 NonlinearSolveNLsolveExt = ["NLsolve", "LineSearches"]
-NonlinearSolvePETScExt = ["PETSc", "MPI"]
+NonlinearSolvePETScExt = ["PETSc", "MPI", "SparseArrays"]
 NonlinearSolveSIAMFANLEquationsExt = "SIAMFANLEquations"
 NonlinearSolveSpeedMappingExt = "SpeedMapping"
 NonlinearSolveSundialsExt = "Sundials"
@@ -104,6 +105,7 @@ Reexport = "1.2.2"
 SIAMFANLEquations = "1.0.1"
 SciMLBase = "2.69"
 SimpleNonlinearSolve = "2.1"
+SparseArrays = "1.10"
 SparseConnectivityTracer = "0.6.5"
 SparseMatrixColorings = "0.4.5"
 SpeedMapping = "0.3"