Integrate BLIS into existing test suite

- Remove standalone test script as requested
- Add BLIS to basictests.jl alongside other factorization algorithms
- Load blis_jll and LAPACK_jll to trigger extension
- Use try/catch to gracefully handle when BLIS extension unavailable
- BLIS will now be tested with the same comprehensive test suite
  as other factorization algorithms

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

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

Author: claude

test/basictests.jl

@@ -2,6 +2,9 @@ using LinearSolve, LinearAlgebra, SparseArrays, MultiFloats, ForwardDiff
 using SciMLOperators, RecursiveFactorization, Sparspak, FastLapackInterface
 using IterativeSolvers, KrylovKit, MKL_jll, KrylovPreconditioners
 using Test
+
+# Import JLL packages for extensions
+using blis_jll, LAPACK_jll
 import Random
 
 const Dual64 = ForwardDiff.Dual{Nothing, Float64, 1}
@@ -227,6 +230,13 @@ end
     if LinearSolve.usemkl
         push!(test_algs, MKLLUFactorization())
     end
+    
+    # Add BLIS when the extension is available
+    try
+        push!(test_algs, LinearSolve.BLISLUFactorization())
+    catch
+        # BLIS extension not available, skip
+    end
 
     @testset "Concrete Factorizations" begin
         for alg in test_algs