Fix init_cacheval for SizedMatrix (StaticArrays.LU has no field factors)

[ChrisRackauckas-Claude]

Problem

init(LinearProblem(A, b)) with a SizedMatrix (StaticArrays) throws on GenericLUFactorization (the default for small dense systems):

FieldError: type StaticArrays.LU has no field `factors`, available fields: `L`, `U`, `p`
  @ StaticArrays/src/lu.jl:20
init_cacheval(::GenericLUFactorization, A::SizedMatrix{9,9}, ...) @ LinearSolve/src/factorization.jl:346

#1038 ("Handle dense, contiguous non-Array matrices (e.g. FixedSizeArray)") changed init_cacheval(::GenericLUFactorization, ...) and init_cacheval(::RFLUFactorization, ...) from

return ArrayInterface.lu_instance(convert(AbstractMatrix, A)), ipiv

to

luinst = ArrayInterface.lu_instance(convert(AbstractMatrix, A))
return LinearAlgebra.LU(luinst.factors, ipiv, luinst.info), ipiv

This assumes lu_instance always returns a LinearAlgebra.LU (fields factors/ipiv/info). For a SizedMatrix, ArrayInterface.lu_instance returns a StaticArrays.LU (fields L/U/p), so luinst.factors errors.

Fix

Guard the LinearAlgebra.LU rebuild: when lu_instance returns something that is not a LinearAlgebra.LU (e.g. a StaticArrays.LU), return it as-is — the pre-#1038 behavior, which already carried a Vector pivot for these containers. The FixedSizeArray case from #1038 (where lu_instance does return a LinearAlgebra.LU but with a container-typed pivot) still takes the rebuild path, so its fix is preserved.

luinst = ArrayInterface.lu_instance(convert(AbstractMatrix, A))
luinst isa LinearAlgebra.LU || return luinst, ipiv
return LinearAlgebra.LU(luinst.factors, ipiv, luinst.info), ipiv

Verification (local, Julia 1.10 and 1.12)

• Before: init(LinearProblem(SizedMatrix{9,9}, b)) throws type LU has no field factors on 3.85.2.
• After (this branch, dev'd): init(LinearProblem(SizedMatrix, b)) succeeds; a normal Matrix solve still returns the correct result.
• Runic clean on src/factorization.jl.

This is the root cause of SciML/OrdinaryDiffEq.jl's InterfaceIV master CI failure (sized_matrix_tests.jl, Rodas4 on a SizedMatrix), which OrdinaryDiffEq is temporarily working around by capping LinearSolve at 3.85.1.

Please ignore until reviewed by @ChrisRackauckas