Migrate DiffEqProblemLibrary to SciMLTesting 2.4

[ChrisRackauckas-Claude]

Summary

• migrate root and every QA environment to SciMLTesting 2.4 with default strict checks
• remove committed local [sources] paths and repository-specific QA weakenings
• add rendered public API docs for every sublibrary, preserving definition-site problem docstrings
• scope Documenter completeness to exported public APIs; private helpers are not rendered as user API

Validation

• strict SciMLTesting 2.4 QA passed for the root package and all seven sublibraries
• Core Pkg.test() passed for DiffEqProblemLibrary, DDEProblemLibrary, and ODEProblemLibrary
• all seven Documenter builds, including doctests and public API checks, passed
• Runic 1.7.0 check passed for every tracked Julia file

Ignore until reviewed by @ChrisRackauckas.