Strengthen public API documentation QA

[ChrisRackauckas-Claude]

Ignore this PR until it has been reviewed by @ChrisRackauckas.

Summary

• require SciMLTesting 2.4+ in the root and every subpackage QA environment, remove redundant 2.4-default settings and TOML source paths, and retain only issue-linked or package-specific exceptions
• replace whole-module imports with explicit imports so strict ExplicitImports QA passes without a generic exception
• give package-owned public APIs definition-site SciMLStyle docstrings, render the root module and developer interfaces, and enable strict doctests and exported-binding checks in Documenter
• add focused tests for documented constructors, recursive-array utilities, and the plotting developer interface

The ragged-array JET exception remains narrowly version-gated and tracked by #620. The root Aqua ambiguity exception remains tracked by #326.

Validation

Local checks passed with SciMLTesting 2.6.2 (satisfying the new 2.4 minimum):

• Julia 1.12.6 (+release): root package tests, all three subpackage test suites, root QA, all three subpackage QA suites, strict docs/doctests/rendered-doc checks, and Runic
• Julia 1.10.11 (+1.10): root package tests, all three subpackage test suites, root QA, all three subpackage QA suites, strict docs/doctests/rendered-doc checks, and Runic

Existing issue-linked expected failures remain: root Aqua ambiguities (#326), ragged JET on Julia 1.11+ (#620), and two pre-existing broken ragged/core indexing assertions. No tests were skipped, disabled, or relaxed.

[ChrisRackauckas-Claude]

Repository-owned CI checks are green. The broad integration failures also occur with clean RecursiveArrayTools master 88fc415 and were reproduced locally in isolated worktrees, so I have kept those unrelated repairs out of this documentation/QA PR:

• OrdinaryDiffEq structured Jacobian cache error: existing fix Fix build_J_W cache init for structured jac_prototypes OrdinaryDiffEq.jl#3942
• OrdinaryDiffEq community callback mismatch (3π/2 instead of π/2): existing fix Keep callback controller resets opt-in OrdinaryDiffEq.jl#4075
• Rosenbrock23 dropping SLArray labels: Rosenbrock23 drops SLArray labels in out-of-place stage broadcast OrdinaryDiffEq.jl#4178
• SciMLSensitivity Core4 undeclared EnsembleSerial ownership/import: Core4 ensemble tests rely on undeclared EnsembleSerial reexport SciMLSensitivity.jl#1587

No test was skipped, silenced, or loosened.

[ChrisRackauckas-Claude]

Follow-up after completing the remaining clean-base downstream reproductions:

• SciMLSensitivity Core1 on clean SciMLSensitivity master plus pre-PR RecursiveArrayTools 88fc415: 200 passed, 3 errored, 6 broken in 53m17.5s. The two bouncing-ball ReverseDiff/Tracker conversion errors are covered by Preserve AD wrappers in Rosenbrock stages OrdinaryDiffEq.jl#4101; the GaussAdjoint ADTypes error is tracked at GaussAdjoint errors on the new sensealg ADTypes test: ParamJacobianWrapper{true} wraps an ODEFunction{false} (MethodError on 3-arg f) SciMLSensitivity.jl#1586.
• SciMLSensitivity Core2 on the same clean base: 198 passed, 1 errored, 13 broken in 84m22.2s. The ReactantVJP stiff-adjoint Jacobian arity mismatch is now tracked at ReactantVJP stiff adjoint passes four-argument Jacobian to out-of-place calc_J SciMLSensitivity.jl#1588.
• OrdinaryDiffEq InterfaceV reproduces the JLArrays 0.3.2 host-LAPACK Ptr conversion error on pre-PR RecursiveArrayTools; exact JLArrays 0.3.1 passes with both GPUArrays 11.5.8 and 11.5.9. Tracked at JLArrays 0.3.2 breaks InterfaceV implicit solve via host LAPACK Ptr conversion OrdinaryDiffEq.jl#4179.

Together with the earlier clean-base findings (#3942, #4075, #4178, and SciMLSensitivity #1587), these establish that the remaining integration failures are dependency-owner regressions rather than changes introduced by this documentation/QA PR. All repository-owned RecursiveArrayTools checks were green before merge.