fix GPU compat of BrownFullBasicInit

[hexaeder]

This PR adds a simple (mutating) DAE as a testcase for GPU compat. Mainly fixes BrownInit for mutating DAEs with mass matrix and cu arrays.

Not tested:

• sparse jac_prototype does not work, fails in rosenbrock init because of Default algs for CUSPARSE failing LinearSolve.jl#827 (comment)
• non-mutating still not working. I tried to fix it but it seems more complicated. But I guess most people using GPUs will use the mutating version anyway.

EDIT: the spares jacobian additionaly fails because

OrdinaryDiffEq.jl/lib/OrdinaryDiffEqNonlinearSolve/src/initialize_dae.jl

Lines 387 to 390 in e038be1

	function algebraic_jacobian(jac_prototype::T, algebraic_eqs,
	algebraic_vars) where {T <: AbstractMatrix}
	jac_prototype[algebraic_eqs, algebraic_vars]
	end

does not work for sparse cuda matrices (this type of indexing is not implemented).

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

[ChrisRackauckas]

Suggested change

	algebraic_vars = mapreduce(iszero, &, M, dims = 1)[:]
	algebraic_eqs = mapreduce(iszero, &, M, dims = 2)[:]
	algebraic_vars = mapreduce(iszero, &, M, dims = 1)
	algebraic_eqs = mapreduce(iszero, &, M, dims = 2)

Is that part needed?

[hexaeder]

yes i think so, otherwise those are not vectors but 1xN and Nx1 matrices, the rest of the code assumes vectors. But i'll check again

[hexaeder]

the vector is indeed needed. I changed it to

    algebraic_vars = vec(all(iszero, M, dims = 1))
    algebraic_eqs = vec(all(iszero, M, dims = 2))

which is more readable and faster.

[hexaeder]

Hm the new testcase fails in CI
https://buildkite.com/julialang/ordinarydiffeq-dot-jl/builds/8192/steps/canvas?sid=019aa1ce-b926-4ba0-82a1-f53ccbd76d9c#019aa1ce-b96d-4508-be39-37f7bed45b39/495-1319

weird, can't reproduce this locally, there the fix works

[ChrisRackauckas-Claude]

Rebased version created at #2941 with resolved merge conflicts and added sources for the new test dependencies (OrdinaryDiffEqNonlinearSolve and OrdinaryDiffEqRosenbrock) to ensure proper package resolution.