Enable rendered public API docs QA

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

• Enable SciMLTesting API documentation QA with api_docs_kwargs = (; rendered = true).
• Add Aqua as a direct dependency of the QA test environment so Aqua's ambiguity subprocess can load it under test/qa.

Audit

• Checked current origin/master exports/public declarations. No package-owned exported names were missing source docstrings.
• No dependency-owned reexports were identified, so no rendered_ignore entries were added.

Validation

• timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=test/qa test/qa/qa.jl
• timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=docs -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate(); include("docs/make.jl")'
• timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=. -e 'using Runic; exit(Runic.main(["--check", "test/qa/qa.jl"]))'
• git diff --check
• Direct source docstring audit checked 61 exported package names with no missing source docstrings.

[ChrisRackauckas-Claude]

CI triage for remaining failures on agent/public-docs-qa-audit at a8a0995b62b09b39a051361a825b4cff212a8989:

• No code change made. The docs build, package tests, QA lane, Runic format check, downgrade, spellcheck, and normal downstream matrix are passing.
• runic-suggestions / Runic Suggestions is not a formatting failure. The log shows Runic checked 33 files successfully, including test/qa/qa.jl, then reviewdog failed while fetching the PR diff: GET https://api.github.com/repos/SciML/SymbolicIndexingInterface.jl/pulls/171: 503 [].
• The four failing IntegrationTest downstream jobs (SciMLBase.jl, Symbolics.jl, RecursiveArrayTools.jl, ModelingToolkit.jl) fail before Julia setup/tests, during actions/checkout of the downstream repository. Logs show GitHub's Unicorn! HTML and No server is currently available to service your request while retrieving the downstream default branch, followed by the checkout step failing.

Focused local validation:

• timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=. -e 'using Runic; exit(Runic.main(["--check", "test/qa/qa.jl"]))' passed with exit code 0.
• timeout 3600 /home/crackauc/.juliaup/bin/julia +1.10 --project=test/qa -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate(); include("test/qa/qa.jl")' passed: Quality Assurance | 17 17.
• git diff --check passed.

Conclusion: remaining failures are GitHub service/API/transient checkout failures, not docs/docstring/rendered-public-API QA failures and not in scope for a code change in this PR.