Enforce strict QA and document HighDimPDE APIs

[ChrisRackauckas-Claude]

Summary

• upgrade QA environments to SciMLTesting 2.4 with default strict checks
• remove dependency reexports and document public and developer APIs at their definitions
• add rendered public API and SciMLBase-style interface documentation

Verification

• Pkg.test() passed: all Core test sets, including DeepBSDE, DeepSplitting, MLP, NNKolmogorov, NNParamKolmogorov, NNStopping, and ProblemConstructor
• strict QA: 20/20 passed
• Documenter doctests and checkdocs = :exports passed
• git diff --check passed

Ignore until reviewed by @ChrisRackauckas.