Update QA to SciMLTesting 2.1 docs checks

[ChrisRackauckas-Claude]

Ignore this draft PR until reviewed by @ChrisRackauckas.

Summary

• Update SciMLTesting compat to 2.1.
• Remove the repo-local QA [sources] path entry.
• Use SciMLTesting public API docs QA with rendered docs checking and reexport handling.
• Add missing NeuralPDE-owned docstrings and rendered docs entries.

Validation

• Runic --check on changed Julia files passed.
• TOML.parsefile over assigned Project.toml files passed.
• GROUP=QA julia +1.11 --project=. -e "using Pkg; Pkg.test()" passed: QA/qa.jl 16 passed, 1 broken, 17 total.