Enable rendered public API docs QA

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

• Enable SciMLTesting rendered public API docs QA via api_docs_kwargs = (; rendered = true).
• Keep the change scoped to the QA invocation; exported package-owned API docstrings and rendered @docs entries were already present.
• Do not add [sources] or path source entries to tracked project files.

Validation

• git diff --check
• julia +1.10 via juliaup shim, Runic.jl formatter check on test/qa/qa.jl
• julia +1.10 --project=docs docs/make.jl
• julia +1.10 --project=test/qa test/qa/qa.jl (16 pass, 1 expected broken)
• julia +1.10 --project=. -e 'using Pkg; Pkg.test(; test_args = ["QA"])' passed, but the harness ran Core tests rather than only QA\n