Use SciMLTesting public API docs QA

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

• Update the package QA/docs coverage branch for SciMLTesting v2.1 public API documentation checks.
• Remove or avoid package self [sources] path entries in the touched QA/docs environments.
• Keep this draft while the fleet-wide public/exported API documentation audit is reviewed.

Validation

• Branch worktree was clean before opening this PR.
• Local validation was run by the worker before push where applicable; this PR-opening pass did not rerun the full package test suite.