Use SciMLTesting 2.1 QA docs check

[ChrisRackauckas-Claude]

This PR should be ignored until reviewed by @ChrisRackauckas.

Summary

• Updates SciMLTesting compat entries to 2.1.
• Enables the shared SciMLTesting rendered public API docs QA check.
• Adds missing public API docstrings/docs rendering needed by the shared check.

Validation

• Runic check on changed Julia files.
• TOML parse check on edited Project files.
• Local QA group with GROUP=QA timeout 3600.