Restore DelayDiffEq extension hooks as public API

[ChrisRackauckas-Claude]

Ignore until reviewed by @ChrisRackauckas.

Summary

• Restore the ten extension hooks that DelayDiffEq already consumed as public API before they were accidentally demoted by Document public developer APIs #3832.
• Make the two later limiter hooks used by DelayDiffEq public.
• Document all twelve hooks in the developer API reference and add owner-package Base.ispublic regression tests.
• Remove the two owner-side ExplicitImports ignores that are obsolete once the API declarations are restored. This does not add or widen any DelayDiffEq QA allowlist.

Root cause

#3832 split the public and developer API documentation, but it also demoted cross-sublibrary hooks while DelayDiffEq continued to use them. A history bisect identifies e1db9b088674f7804a971100210631ac0c801104 from that PR as the first bad commit.

Ten names are restorations of the preexisting public surface. resolve_stage_step_limiters and trivial_limiter! were introduced after that demotion and are additive APIs in the already-unreleased OrdinaryDiffEqCore 4.12.0 release; current General has OrdinaryDiffEqCore 4.11.0.

Dependency

This PR depends on #4066 for the clean current-master test environment to resolve. The resolver change is intentionally not duplicated here.

Validation

• GROUP=DelayDiffEq_QA on Julia 1.12, stacked on Restore SciMLBase 3.39 compatibility for owner imports #4066: clean baseline was 17 passed / 2 errored (exit 1); this patch is 19/19 passed (exit 0), with the same SciMLTesting 2.6.1, ExplicitImports 1.15.0, and SciMLBase 3.39.1 dependencies.
• GROUP=OrdinaryDiffEqCore_QA on Julia 1.12: passed (exit 0).
• GROUP=OrdinaryDiffEqNonlinearSolve_QA on Julia 1.12: passed (exit 0).
• Documentation instantiate and build on Julia 1.12: passed (exit 0).
• Runic over the changed files: passed. Full-repository Runic also passed with the exact patch stacked on the existing formatting prerequisite Run Runic on the disco-optimizations files #4064 and resolver prerequisite Restore SciMLBase 3.39 compatibility for owner imports #4066.

GROUP=OrdinaryDiffEqDefault_QA still reports the independent lorenz_pref / lorenz_pref_params private-helper access on both this branch and a clean e5489faa + #4066 control (18 passed / 1 errored, exit 1). That preexisting failure is deliberately not folded into this focused API-restoration PR.

[ChrisRackauckas-Claude]

Investigation scratchpad:

1. Reproduced the current DelayDiffEq QA failure on clean e5489faa + resolver prerequisite Restore SciMLBase 3.39 compatibility for owner imports #4066.
2. Bisected the API regression to e1db9b088674f7804a971100210631ac0c801104 (Document public developer APIs #3832).
3. Restored declarations at the owning sublibraries, rendered every public name in the developer docs, and added owner-package Base.ispublic tests.
4. Verified the exact seven-file patch with DelayDiffEq/Core/NonlinearSolve QA, docs, and Runic; kept the independent Default precompile-helper failure out of scope.

[ChrisRackauckas-Claude]

CI dependency note: the two immediate downgrade failures (GlobalDiffEq and OrdinaryDiffEqExtrapolation) stop in Resolver.jl with Unsatisfiable on this unstacked branch. The corresponding downgrade jobs pass on prerequisite #4066 (3m01s and 9m02s respectively). No change is warranted in this focused PR; the #4066 dependency is declared in the description.