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.

[ChrisRackauckas-Claude]

CI triage note: the only red check is tests / Core (julia lts, macos-latest) / Tests - Core (Julia lts) from https://github.com/SciML/SurrogatesBase.jl/actions/runs/29150679972/job/86539745129.

The check-run annotations show a GitHub timeout, not a Julia test failure:

The job has exceeded the maximum execution time of 2h0m0s

The log enters julia-actions/julia-runtest and then has no Julia failure output before cancellation. All other checks are green, including docs, downgrade, Runic, Ubuntu/Windows lts core, Julia 1/pre core on all platforms, and QA. This looks like a macOS lts runner timeout that needs a rerun rather than a code change in this PR.