Add ElementalJL solver wrapper

[AJ0070]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Closes #47. Adds ElementalJL wrapper

What's added

• src/extension_algs.jl: ElementalJL <: AbstractDenseFactorization struct with keyword argument method ∈ {:LU, :QR, :Cholesky} and a full docstring.
• ext/LinearSolveElementalExt.jl: package extension implementing init_cacheval and solve!. Handles AbstractMatrix and Elemental.Matrix inputs, promotes non-native element types to Float64/ComplexF64.
• Project.toml: Elemental = "0.6" registered in [weakdeps], [extensions], [compat], [extras], and [targets].
• export ElementalJL in src/LinearSolve.jl.
• test/elemental/elemental.jl + test/elemental/Project.toml: standalone test sub-project covering LU, QR, Cholesky, Float32, ComplexF64, direct Elemental.Matrix input, cache reuse, and a regression test for in-place mutation safety.
• .github/workflows/Tests.yml: LinearSolveElemental CI group, Windows excluded (no Elemental_jll binary for x86_64-w64-mingw32).

AI disclosure: Used Claude to support development by writing code, documenting non-trivial logic with docstrings and comments, and creating comprehensive test coverage. Used Chatgpt to format PR description in markdown.

[AJ0070]

relying on CI for tests outputs because currently I don't have access to my ubuntu machine and ElemetalJL doesn't have windows binary. I will ping for review once all relevant tests pass successfully.

[AJ0070]

now tests should pass successfully. currently working on lq support

[AJ0070]

@andreasnoack the lq! support added in JuliaParallel/Elemental.jl#83 was never included in a tagged release; the registered version is still v0.6.0 (pre- JuliaParallel/Elemental.jl#83), so downstream packages like LinearSolve.jl (@ChrisRackauckas) can't use it natively.
Could you cut a v0.6.1 release?

[andreasnoack]

I've starting looking into it, but it looks like CI hasn't run in long time. (Was configured for Travis). I've started JuliaParallel/Elemental.jl#84 and Claude is chipping away on analysing the errors there.

[AJ0070]

@andreasnoack please let me know if you need any help with it.

[AJ0070]

@ChrisRackauckas I have kept this on hold and have started working on MUMPS wrapper.

[AJ0070]

@ChrisRackauckas Is there a blocker preventing this?

[ChrisRackauckas]

Just the new covid variant lol

[AJ0070]

please take care