exp: Padé denominator solve via LinearSolve default algorithm (alias_A)

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas. Draft; opened by an agent at Chris's direction.

Switches ExpMethodHigham2005Base's cached Padé denominator solve from LinearSolve's default algorithm to GESVFactorization (SciML/LinearSolve.jl#1078, v4.3.0): one combined gesv! per refactorization, restoring raw-LAPACK parity at small n (−1.8% vs the original gesv! code at n=5, ties within noise at n=10–250; bit-identical accuracy and allocation bytes across all 12 benchmark cells). Also restores the historical SingularException contract — the default algorithm's QR safety-fallback silently resolved singular denominators.

Compat: LinearSolve = "4.2" — unmergeable until LinearSolve 4.3.0 tags (#1078). Full EU basictests pass locally against the dev'd branch (22 testsets, 1 pre-existing broken).

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

LinearSolve 4.3.0 (with GESVFactorization, SciML/LinearSolve.jl#1078) is released. Rebased onto current master and bumped compat to LinearSolve = "4.3". Verified locally against 4.3.0: exp! ≈ Base.exp to 2.3e-15, exp-methods testset 40/40, Phi testset 284/284. Ready for CI once the registry propagates 4.3.0.

[ChrisRackauckas-Claude]

Switched from GESVFactorization to LinearSolve's default algorithm choice (with alias_A/alias_b) after re-benchmarking with matched aliasing — thanks @ChrisRackauckas for pushing on this.

With alias_A = true the default:

• is allocation-competitive (no O(n²) backup copy — my earlier "+2–4.5%" was measured without alias on the default, an unfair comparison);
• has a 2–2.7× faster solve at small/medium n when RecursiveFactorization is loaded (RFLU beats LAPACK LU — the common case in exponential-integrator stacks), vs GESV/LU which are pinned to LAPACK;
• needs only LinearSolve 4.1 (alias_A in-place refactorization), not the 4.3-only GESVFactorization — so compat dropped "4.3" → "4.1" and this no longer waits on the latest release;
• auto-benefits from future LinearSolve algorithm improvements.

Singular-denominator behavior is unchanged: the solve returns a Failure retcode, which the code converts back to the SingularException exp! has always thrown.

Verified against registered LinearSolve 4.1.0: exp! ≈ Base.exp to ~2e-15, exp-methods testset 40/40, Phi testset 284/284. (GESVFactorization remains a useful general-purpose LinearSolve alg from #1078 regardless — it's just not the optimal pick for this fresh-every-call pattern.)