Make Core5 parameter_handling u0 Float32-homogeneous (fixes LuxLib mixed-precision warning)

[ChrisRackauckas-Claude]

Please ignore until reviewed by @ChrisRackauckas.

Summary

test/Core5/parameter_handling.jl built NonlinearProblem / ODEProblem states with default Float64 zeros/ones while Lux parameters in the ComponentArray are Float32. That mismatch triggers LuxLib's mixed-precision matmul_cpu_fallback! warning, which fails @test_nowarn. This change makes the three state constructions Float32 so they match the existing x = ones(Float32, 2, 3) and Lux params. No production code changed; @test_nowarn is intentionally left strict.

Closes #1609

Verification

Scratch env (Pkg.develop of this repo + Lux, ComponentArrays, NonlinearSolve, OrdinaryDiffEq, Zygote, Test), Julia 1.12.7:

export TMPDIR=/home/crackauc/sandbox/goals/issue-backlog/ibd/SciMLSensitivity.jl/jobs/1609-cursor/tmp
export JULIA_DEPOT_PATH=.../jobs/1609-cursor/depot:$HOME/.julia
julia +1.12 --project=.../scratch/ph_env test/Core5/parameter_handling.jl

Before (unmodified master contents of the test file)

[ Info: Testing Nonlinear Solve Adjoint with Nested Parameters
┌ Warning: Mixed-Precision `matmul_cpu_fallback!` detected and Octavian.jl cannot be used for this set of inputs (C [Matrix{Float64}]: A [Base.ReshapedArray{Float32, 2, SubArray{Float32, 1, Vector{Float32}, Tuple{UnitRange{Int64}}, true}, Tuple{}}] x B [Matrix{Float64}]). Falling back to generic implementation. This may be slow.
└ @ LuxLib.Impl ~/.julia/packages/LuxLib/zPBrt/src/impl/matmul.jl:194
Test Failed at .../Test.jl:934
  Expression: contains_warn(...)
ERROR: LoadError: There was an error during testing
in expression starting at .../test/Core5/parameter_handling.jl:17

After (this PR)

[ Info: Testing Nonlinear Solve Adjoint with Nested Parameters
[ Info: Testing Gauss Adjoint with Nested Parameters

(exit code 0; both @test_nowarn paths and nested Zygote gradients completed)

Also: Runic --check and typos on the touched file both exit 0.

Not verified

• Full GROUP=Core5 / Pkg.test() suite (only this file was run, to keep load down on a busy machine).
• Downstream OrdinaryDiffEq IntegrationTest CI that originally surfaced the failure.

Reviewer push-back

• Whether any callers intentionally want mixed Float64 state / Float32 Lux params (this PR only fixes the test boundary, not library behavior).
• Whether Float32 tolerance / adjoint numerics need an explicit absolute/relative check beyond @test_nowarn and non-nothing gradients (existing assertions kept as-is).

Risk assessment

• Risk: low
• Blast radius: one Core5 test file only; no src/ changes
• Evidence: fail-before / pass-after on parameter_handling.jl with the mixed-precision warning present then absent
• Independent review: Claude Code (Opus 5.5) rated it low, high confidence: master 9 pass / 1 fail (LuxLib mixed-precision warning at line 17), PR 10/10 with no warnings; the Float64 enters from the test's own u0, not SciMLSensitivity (both @test_nowarn calls are plain forward solves); the ODE hunk is also needed — LuxLib logs the warning with maxlog=1, so master's ODE @test_nowarn passed only by accident and fails when run alone.
• Merge: auto-merge candidate once CI shows no regressions (test-only, 3 lines; author and reviewer both low).

Please ignore this draft until reviewed by @ChrisRackauckas.

Harness: Cursor Agent CLI 2026.09.28-64d2043; model: auto; transcript: /home/crackauc/sandbox/goals/issue-backlog/ibd/SciMLSensitivity.jl/jobs/1609-cursor/log.txt on amdci2.julia.csail.mit.edu