Fix type check for mixed precision methods in tests

Use string matching to detect mixed precision methods instead of Union type
to avoid issues with type availability during test compilation.

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

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

Author: ChrisRackauckas

test/nopre/caching_allocation_tests.jl

@@ -1,8 +1,6 @@
 using LinearSolve, LinearAlgebra, SparseArrays, Test, StableRNGs
 using AllocCheck
-using LinearSolve: AbstractDenseFactorization, AbstractSparseFactorization,
-                   MKL32MixedLUFactorization, OpenBLAS32MixedLUFactorization,
-                   AppleAccelerate32MixedLUFactorization, RF32MixedLUFactorization
+using LinearSolve: AbstractDenseFactorization, AbstractSparseFactorization
 using InteractiveUtils
 
 rng = StableRNG(123)
@@ -58,10 +56,8 @@ rng = StableRNG(123)
             end
 
             # Mixed precision methods need looser tolerance
-            is_mixed_precision = alg isa Union{MKL32MixedLUFactorization, 
-                                                OpenBLAS32MixedLUFactorization,
-                                                AppleAccelerate32MixedLUFactorization,
-                                                RF32MixedLUFactorization}
+            # Check if algorithm name contains "32Mixed"
+            is_mixed_precision = occursin("32Mixed", string(typeof(alg)))
             tol = is_mixed_precision ? 1e-5 : 1e-10
 
             # Initialize the cache