FFS - REFACTOR - Extract local stability into standalone LocalStability module (refactor plan PR 2)

[matt-pharr]

PR 2 of the refactor sequence in REFACTOR_PLAN.md (§4). Stacked on #381 (refactor/riccati-unification) — this PR shows only the LocalStability extraction; review/merge #381 first. When #381 merges and its branch is deleted, GitHub retargets this PR to develop. The remaining work (original PRs 3–5) lands as a single combined interface PR on refactor/forcefreestates-result, stacked on this one.

What this does

• Moves Ballooning.jl (Mercier D_I, resistive interchange D_R, high-n ballooning Δ′ scans and s–α drivers) out of ForceFreeStates into a new top-level LocalStability module via git mv (history preserved).
• LocalStability depends only on Equilibrium plus math libraries — no stability-solver state. The HDF5 group LocalStability/* (from ALL - REFACTOR - Module-mirroring CamelCase HDF5 schema (issue #226, PR A) #363) already matches the module name, so no dataset paths change.
• Every entry point drops the ForceFreeStatesControl argument (it only ever supplied verbose) in favor of a verbose::Bool=false kwarg: compute_local_stability(equil; verbose), ballooning_alpha_boundary(equil; …), ballooning_alpha_boundaries, ballooning_qprime_boundaries, scan_delta_prime_map, ballooning_delta_prime_map, ballooning_qprime_delta_prime_map, compute_ballooning_stability!.
• ctrl.local_stability_flag stays in [ForceFreeStates] (the driver reads it); a [LocalStability] TOML section is deliberately out of scope.
• Updated call sites: driver (main_from_inputs), test/runtests_resist_eval.jl, examples/DIIID-like_ideal_example/analyze_example.jl (also sheds a throwaway ForceFreeStatesControl construction), Analysis docstring cross-references.
• Docs: Ballooning.jl removed from stability.md's @autodocs Pages; new @autodocs block for LocalStability in ballooning.md (satisfies checkdocs=:exports); architecture.md module list/dependency tree updated to eight modules.

No numerical changes: pure code motion plus signature mechanics.

Verification

• runtests_resist_eval.jl 63/63 and runtests_fullruns.jl 17/17 pass on this tree; zero stale ForceFreeStates.*ballooning* references (grep across src/test/examples/benchmarks/docs).
• Full test suite
• Docs build (build_docs_local.jl)
• Regression harness vs stack base (--refs refactor/riccati-unification,local; expected: LocalStability/* datasets identical) — pasted here before this PR leaves draft

⚠️ Review requirement

This PR must not be merged without a third-party human reviewer's approval — non-negotiable (see REFACTOR_PLAN.md §8).

🤖 Generated with Claude Code

[logan-nc]

Another great re-org.
Human diff review complete - are you happy Claude??

[logan-nc]

@matt-pharr I assigned you to hit merge in case there was a fancy ordering you preferred for your PRs

[logan-nc]

🚀