Add vector right-hand-side ldiv! dispatch

[ChrisRackauckas-Claude]

⚠️ Draft — please ignore until reviewed by @ChrisRackauckas.

Adds first-class vector right-hand-side ldiv! methods for all four wrapper types (2- and 3-arg, Val thread flag), prompted by the measurement in SciML/LinearSolve.jl#1161 that the TriangularSolve matrix kernels tie a hand-written scalar back-solve and beat getrs! for nrhs == 1 once the native upper kernel exists.

Design

No reshape, no new kernel: the left-division paths already work on transpose(A), and for a vector b the required 1×n transposed operand is just transpose(b) — a stack immutable, so the whole path stays zero-allocation (a reshape(b, :, 1) header would allocate). With M = 1 the drivers run their scalar row-remainder sweep.

That sweep beats BLAS trsv while the triangle is cache-resident but loses to trsv's blocked sweep beyond L2, so the methods defer to LinearAlgebra above VECTOR_RHS_CUTOFF = 128:

per-leg, min times, Float64, 1 BLAS thread (EPYC 7502 / AVX2, ns)
   n  |  trsv-U    TS-U   ratio |  trsv-unitL  TS-unitL  ratio
    8 |    229      129    1.78 |     190         80      2.38
   16 |    390      249    1.57 |     270        179      1.51
   32 |    709      480    1.48 |     529        399      1.33
   64 |   1390     1029    1.35 |    1100        850      1.29
  128 |   3290     2470    1.33 |    2760       2320      1.19
  --- cutoff: kernels above this line, LinearAlgebra below ---
  256 |   8760     8730    1.00 |    7820       7890      0.99
  512 |  29899    29940    1.00 |   28920      29250      0.99
 1000 |  97480   101980    0.96 |  100390      95179      1.05

(Without the cutoff the kernel path degrades to 0.44x at n = 512 — measured before adding it; the cutoff keeps every size at parity or better vs current behavior.)

Verification

• Full suite TriangularSolve.jl | 149168 149168 pass (Julia 1.12.4), Aqua + ambiguities clean. New testset sweeps n ∈ {1..500} straddling the cutoff, all four wrappers, both Val flags, 2-/3-arg, Float32/64, packed-lu! parent, and asserts zero allocations on the kernel path.
• Failing-before: on main, which(TriangularSolve.ldiv!, (UpperTriangular{Float64,Matrix{Float64}}, Vector{Float64}, Val{false})) is the catch-all; with this PR it is a native method (and the n ≤ 128 timings above are the behavior change).
• Not verified: AVX-512/aarch64 (cutoff chosen from this machine's L2; it is conservative — the scalar sweep is ISA-independent while trsv improves with wider vectors, so the crossover should not move much upward).

Reviewer notes

• The cutoff is a hardware-flavored constant; happy to make it Float32-specific or derive it from VectorizationBase.cache_size if you prefer.
• rdiv! with a vector is not added — LinearAlgebra has no such method surface for triangular right-division, so there is nothing to mirror.
• Independent of Inline the backward panel kernels into the driver #46 (disjoint file regions; either merges first without conflict).

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.69%. Comparing base (e4d4714) to head (24abdb7).
⚠️ Report is 6 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #47      +/-   ##
==========================================
+ Coverage   94.62%   94.69%   +0.07%     
==========================================
  Files           1        1              
  Lines         837      849      +12     
==========================================
+ Hits          792      804      +12     
  Misses         45       45              

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.