Fix master QA failures: restore Differentiation public API, add missing docstrings

[ChrisRackauckas-Claude]

Please ignore this PR until reviewed by @ChrisRackauckas.

Summary

Fixes two pre-existing test failures on unmodified master (aa895b5):

1. lib/OrdinaryDiffEqRosenbrock QA group: all_explicit_imports_are_public errored on 12 names imported from OrdinaryDiffEqDifferentiation (build_J_W, build_grad_config, build_jac_config, calc_rosenbrock_differentiation[!], calc_tderivative, dolinsolve, issuccess_W, jacobian2W!, resize_grad_config!, resize_jac_config!, wrapprecs), and public API has docstrings failed on HybridExplicitImplicitRK.
2. lib/OrdinaryDiffEqRosenbrockTableaus default suite: public API has docstrings failed on 8 undocumented exports.

Root causes (git blame, no bisect needed)

• De-publicized Differentiation API: e1db9b0 (Document public developer APIs #3832, "Split public and developer API docs", 2026-07-10) removed the Expr(:public, ...) block from OrdinaryDiffEqDifferentiation and dropped its Jacobian/W-matrix section from the docs page — but eight sublibraries (OrdinaryDiffEqRosenbrock, OrdinaryDiffEqFIRK, OrdinaryDiffEqSDIRK, OrdinaryDiffEqExtrapolation, OrdinaryDiffEqStabilizedIRK, OrdinaryDiffEqExponentialRK, OrdinaryDiffEqNonlinearSolve, StochasticDiffEqImplicit) still explicitly import those names, and their QA all_explicit_imports_are_public checks (plus the qa.jl header comments from ExplicitImports: drive sublibrary QA checks to green (ei_broken markers) #3776) rely on them being public. Restoring the public block fixes the confirmed Rosenbrock failure and should fix the same latent failure in the other consumers.
• Undocumented exports: latent since HybridExplicitImplicitRK was exported without a docstring in 1c68eff (2026-02-22) and since the tableau sublibrary extraction (25dc6e8/32a53ca5, April 2026) exported 8 tableau names without docstrings. They only started failing when 12b6996 (Update SciMLTesting QA docs coverage #3867, 2026-07-11) upgraded the QA infrastructure to SciMLTesting 2.1, which introduced the public API has docstrings check. So the trigger was the new SciMLTesting check, not a recent source regression.

Changes

• Restore the Expr(:public, ...) block (20 names) in OrdinaryDiffEqDifferentiation — all 20 still had their docstrings from Document public API: add docstrings + docs entries #3858 — plus the corresponding @docs section in docs/src/devtools/internals/public_api.md and the using/modules wiring in docs/make.jl.
• Add devtools/internals/public_api.md to size_threshold_ignore: with the restored entries the page renders at 202.6 KiB, just over Documenter's 200 KiB default (same treatment as the two large Rosenbrock pages).
• Add a docstring for HybridExplicitImplicitRK (following the existing Tsit5DA docstring).
• Add docstrings for RodasTableau, Rodas5Tableau, ROS3PRodasTableau, RosShamp4RodasTableau, Velds4RodasTableau, GRK4ARodasTableau, ROS2PRRodasTableau, ROS34PW1bRodasTableau (matching the existing short style, e.g. Rodas4Tableau).
• Version bumps: OrdinaryDiffEqDifferentiation 3.3.1 → 3.4.0 (restores public names; the removal shipped in 3.3.x), OrdinaryDiffEqRosenbrock 2.4.1 → 2.4.2, OrdinaryDiffEqRosenbrockTableaus 2.2.1 → 2.2.2 (docstrings only).

If the #3832 de-publicization of the Differentiation solver-author API was intentional, the alternative fix is adding these names to the ExplicitImports ignore lists of all eight consumer sublibs — happy to switch, but restoring publicness matches the qa.jl header comments and the #3776 design.

Verification (all run locally on this branch)

• ODEDIFFEQ_TEST_GROUP=QA Pkg.test() in lib/OrdinaryDiffEqRosenbrock: passed — Aqua 19/19 (was 17 pass / 1 fail / 1 error on master).
• Pkg.test() in lib/OrdinaryDiffEqRosenbrockTableaus: passed — Quality Assurance 19/19 (was 18/1 fail), convergence 335/335.
• Full docs build (julia --project=docs docs/make.jl): exited 0; rendered public_api page contains the restored Differentiation entries.
• Standalone check: Base.ispublic(OrdinaryDiffEqDifferentiation, n) == true for restored names; Docs.undocumented_names(OrdinaryDiffEqRosenbrockTableaus) clean.
• julia -m Runic --check passes on all changed files.

Note: #3931 (rodas3d) also touches lib/OrdinaryDiffEqRosenbrock and lib/OrdinaryDiffEqRosenbrockTableaus; the tableau-file docstring additions here may produce a trivial merge conflict with it.

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[ChrisRackauckas-Claude]

CI triage

This PR's targets are green: lib/OrdinaryDiffEqRosenbrock [QA] and lib/OrdinaryDiffEqRosenbrockTableaus [QA] both pass on this PR (both failed on merged #3921 / current master).

Triage of the remaining failures, compared check-by-check against merged PR #3921 (= master aa895b5):

1. Other sublibrary [QA] jobs (DelayDiffEq, BDF, ExponentialRK, Extrapolation, FIRK, IMEXMultistep, NonlinearSolve, PDIRK, StabilizedIRK, StochasticDiffEqImplicit/Leaping/Weak) — pre-existing, not caused by this PR

Every one of these also failed on #3921. They run here only because the Differentiation change triggers path-filtered CI for its dependents. Spot-checked lib/OrdinaryDiffEqFIRK [QA]: it fails all_explicit_imports_are_public on OrdinaryDiffEqCore names, e.g.

PredictiveControllerCache is not public in OrdinaryDiffEqCore but it was imported ... at lib/OrdinaryDiffEqFIRK/src/OrdinaryDiffEqFIRK.jl:47

That is the same root cause as the Rosenbrock failure fixed here — #3832 (e1db9b0) also removed a set of OrdinaryDiffEqCore names from Core's public block (PredictiveControllerCache, IControllerCache, get_fsalfirstlast, cache types, etc.) while consumers still import them. Scope decision: this PR deliberately restores only the OrdinaryDiffEqDifferentiation block (the confirmed Rosenbrock failure); restoring/triaging the trimmed OrdinaryDiffEqCore names touches many more consumers and deserves its own small PR rather than expanding this one.

2. lib/OrdinaryDiffEqBDF / Tests - Core — pre-existing, unrelated

Also failed on #3921. Log shows BDF Inference Tests erroring at test/inference_tests.jl:19 with an @inferred return-type mismatch inside OrdinaryDiffEqNonlinearSolve's NonlinearSolveAlg/TrustRegion cache types — nothing to do with docstrings or public declarations (which have no runtime/inference effect).

3. tests / * (julia lts) groups — known infra issue

All LTS-group failures show Failed to precompile DiffEqDevTools ... UndefVarError: RungeKuttaMethod not defined, the known DiffEqDevTools-on-LTS issue fixed separately in #3939. (Which LTS groups fail varies run to run — #3921 failed Integrators_II, this PR fails other groups — consistent with that issue, not with this change.)

4. downgrade-sublibraries + GPU — chronic, identical failure set to #3921.

Net: no CI failure on this PR is introduced by this change; the two failures it targets are fixed, and it incidentally un-breaks the QA of the other sublibs that import the Differentiation names (their remaining QA failures are the Core-name issue above).

[ChrisRackauckas-Claude]

Findings from an independent investigation of the master QA failures (checkout of 4e1a434), relevant to this PR's approach:

Blast radius confirmation. The de-publicization in #3832 (e1db9b0) breaks QA far beyond Rosenbrock. The full-matrix Sublibrary CI run on master aa895b5 (run link) failed 24 QA jobs: PDIRK, FIRK, LowOrderRK, Extrapolation, BDF, ImplicitDiscreteSolve, NonlinearSolve, ExponentialRK, DelayDiffEq, IMEXMultistep, FunctionMap, StabilizedIRK, Rosenbrock, StochasticDiffEq{RODE,Weak,HighOrder,IIF,LowOrder,Milstein,Implicit,ROCK,Leaping,Core}, and DiffEqDevTools. A grep of the monorepo shows the removed OrdinaryDiffEqNonlinearSolve hooks are explicitly imported by BDF, SDIRK, IMEXMultistep, Multirate, PDIRK, StabilizedIRK, StochasticDiffEq{Implicit,Leaping,Weak}, and DelayDiffEq (nlsolve!, nlsolvefail, compute_step!, anderson, anderson!), and the removed OrdinaryDiffEqDifferentiation names by Extrapolation, FIRK, Rosenbrock, SDIRK, StabilizedIRK, ExponentialRK, and StochasticDiffEqImplicit.

Local reproduction. On master, ODEDIFFEQ_TEST_GROUP=QA for lib/OrdinaryDiffEqStabilizedIRK fails all_explicit_imports_are_public on exactly build_nlsolver, nlsolve!, du_alias_or_new, markfirststage! (OrdinaryDiffEqNonlinearSolve) and dolinsolve, update_W! (OrdinaryDiffEqDifferentiation).

Gap in this PR. This PR restores the OrdinaryDiffEqDifferentiation public block, which fixes the Differentiation-name half everywhere. It does not restore the OrdinaryDiffEqNonlinearSolve hooks (build_nlsolver, nlsolve!, nlsolvefail, compute_step!, initial_η, markfirststage!, du_alias_or_new, anderson, anderson!) that #3832 also removed — those are only addressed by #3912's per-lib ignores, and only in 5 libs there (BDF/SDIRK/Multirate/StochasticDiffEq*/DelayDiffEq are uncovered by either PR). One of the two approaches (restore public in the owner, per this PR, vs. per-lib ignores, per #3912) should be applied consistently to the OrdinaryDiffEqNonlinearSolve names too, or PRs touching those libs will keep failing QA.

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