Construct NonlinearSolution without spelling out its type parameters

[ChrisRackauckas-Claude]

Draft. Ignore this PR until reviewed by @ChrisRackauckas.

What changed and why

SciML/SciMLBase.jl#1563 appends a retcode type parameter to NonlinearSolution, and the three places in this repo that spell out all of its parameters then fail to precompile — which is what #1563's downstream and docs lanes currently show. This makes those sites layout-agnostic so they work with both the released SciMLBase and #1563:

• build_solution_less_specialize (lib/NonlinearSolveBase/src/polyalg.jl) and the SCC solution element type pick the layout once at load time via fieldtype(SciMLBase.NonlinearSolution, :retcode).
• nonlinear_solution_new_alg (lib/SimpleNonlinearSolve/src/utils.jl) uses the positional constructor, which computes the same parameters.

Patch bumps (rebased onto master after the 2.49.0 / 1.15.2 releases): NonlinearSolveBase 2.49.1, SCCNonlinearSolve 1.15.3, SimpleNonlinearSolve 2.14.2. Intended to merge and be released before #1563; carved out of #1197, which will be rebased on it.

Verification

Julia 1.12.4, each sublibrary's own project with the local NonlinearSolveBase developed in:

GROUP=Core  NonlinearSolveBase      Testing NonlinearSolveBase tests passed
GROUP=Core  SCCNonlinearSolve       Testing SCCNonlinearSolve tests passed
GROUP=Core  SimpleNonlinearSolve    Testing SimpleNonlinearSolve tests passed

The same code precompiles and passes the NonlinearSolve Reactant test group against #1563 (that run is in #1197). Runic-formatted; typos clean.

Not verified

• QA groups (the change adds no imports or public names); GPU groups.

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🤖 Generated with Claude Code (model: claude-fable-5) on behalf of Chris Rackauckas. Session: https://claude.ai/code/session_016LsC6pp9z6s5EABX9DnVjE

[ChrisRackauckas-Claude]

CI triage: the only red lane is lib/SimpleNonlinearSolve [QA], failing Aqua's Persistent tasks check (a timing-based check unrelated to the constructor change). The same lane flips on master: failure on SublibraryCI run 33157989116, success on 33157109972. Locally the QA group of SimpleNonlinearSolve passes with these sources (see #1197). I cannot rerun the job from this account.

🤖 Posted by an AI agent (Claude Code, model claude-fable-5) on behalf of Chris Rackauckas. Session: https://claude.ai/code/session_016LsC6pp9z6s5EABX9DnVjE

[ChrisRackauckas-Claude]

CI triage: the three red OrdinaryDiffEq.jl/* downstream lanes fail during environment resolution, not in tests — Unsatisfiable requirements detected for package TimerOutputs: NonlinearSolveBase's compat TimerOutputs = "1" (unchanged here) versus AlgebraicMultigrid's requirement in OrdinaryDiffEq's downstream environment. Nothing in this PR touches dependencies or compat other than the three patch version bumps; the same environment resolves the same way for any current branch (the equivalent lanes on #1197/#1213 are still running). Everything else is green.

🤖 Posted by an AI agent (Claude Code, model claude-fable-5) on behalf of Chris Rackauckas. Session: https://claude.ai/code/session_016LsC6pp9z6s5EABX9DnVjE

[ChrisRackauckas-Claude]

Rebased onto master after the 2.49.1 release (#1221): NonlinearSolveBase is now bumped to 2.49.2 here, the same version #1223 (TimerOutputs compat fix for the master downstream failure) bumps to; whichever merges first, the other needs a one-line rebase.

🤖 Posted by an AI agent (Claude Code, model claude-fable-5) on behalf of Chris Rackauckas. Session: https://claude.ai/code/session_016LsC6pp9z6s5EABX9DnVjE