Require TriangularSolve 0.2.2 for the native upper-triangular ldiv!

[ChrisRackauckas-Claude]

⚠️ Draft — please ignore until reviewed by @ChrisRackauckas.

🚧 Blocked on TriangularSolve 0.2.2 being merged and registered (native upper-triangular ldiv!, prepared at ChrisRackauckas-Claude/TriangularSolve.jl upper-ldiv; spec in SciML/LinearSolve.jl#1146). Until it is registered, CI here fails at Pkg resolution because the 0.2.2 lower bound does not exist yet.

What changed and why

Compat-only: require TriangularSolve = "0.2.2" and bump this package to 0.2.27. TriangularSolve 0.2.2 adds ldiv!(::UpperTriangular, ::AbstractMatrix), so the U leg of the pivotless (NotIPIV) LU ldiv! in src/lu.jl — which already calls TriangularSolve.ldiv! on both legs — now dispatches to a native SIMD kernel instead of silently falling through TriangularSolve's catch-all to BLAS trsm. No code change is needed here.

Verification

Full test suite run locally (Julia 1.12.4, AMD EPYC 7502) with the TriangularSolve upper-ldiv branch Pkg.developed:

Test Summary:         | Pass  Total     Time
Test LU factorization | 3120   3120  2m28.0s

The 🦋 testset errors on this branch and on unmodified master with UndefVarError: mul! not defined in RecursiveFactorization — a pre-existing master breakage introduced by 0e635a2 (see the bisect + one-line fix in #111, which this PR depends on for green CI). It is unrelated to this compat change.

Solve-only kernel benchmark backing the change (Float64, nrhs=8, 1 BLAS thread, EPYC 7502/AVX2; U-leg comparison of LinearAlgebra.ldiv! (BLAS trsm, the old fallback) vs TriangularSolve.ldiv! 0.2.2 native):

  n     trsm        TS native
  64      4.09 us    1.78 us   (2.3x)
  128    12.36 us    6.27 us   (2.0x)
  256    49.18 us   22.04 us   (2.2x)
  500   154.79 us   79.64 us   (1.9x)

What was not verified

• Julia lts/pre lanes (local run was 1.12.4; TriangularSolve itself was validated on 1.10.11 and 1.12.4).
• The 🦋 path (pre-existing failure, fixed separately in Import mul! from LinearAlgebra in butterflylu.jl #111).

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