Kaczmarz tests are failing for sparse entries

[vp314]

Describe the bug
Block Kaczmarz update tests for sparse matrices are failing (see Lines 660 to 697 of Kaczmarz test file). The error and its trace back can be viewed in this GitHub action report and the relevant snippet is copied below.

MethodError: no method matching ldiv!(::LinearAlgebra.AdjointFactorization{Float32, SparseArrays.SPQR.QRSparse{Float32, Int64}}, ::Vector{Float32})
The function `ldiv!` exists, but no method is defined for this combination of argument types.

To Reproduce

• Be sure you are using the most recent version of Julia (1.12.3)
• Pull the main branch. Call julia --project from the root directory.
• Enter Pkg REPL by typing in ] form the REPL.
• Once in Pkg REPL type in test and hit enter.

Expected behavior
The test should produce an error "outside of a test" environment. The error should be

MethodError: no method matching ldiv!(::LinearAlgebra.AdjointFactorization{Float32, SparseArrays.SPQR.QRSparse{Float32, Int64}}, ::Vector{Float32})
The function `ldiv!` exists, but no method is defined for this combination of argument types.

Desktop (please complete the following information):

• OS: Linux
• Julia Version: 1.12.3