Use rendered docs QA in FindFirstFunctions

[ChrisRackauckas-Claude]

Ignore this PR until reviewed by @ChrisRackauckas.

Summary

• Replace the hand-rolled public API documentation coverage test with SciMLTesting's rendered public API docs check.
• Keep strict docs linkcheck working by replacing GitHub HTML links that returned 429 locally with stable raw/hosted URLs.

Validation

• git diff --check passed.
• QA passed with api_docs_kwargs = (; rendered = true): Quality Assurance 18/18.
• Pkg.test() passed: Core/core_tests.jl ran 172201 assertions.
• include("docs/make.jl") passed after the link updates; Documenter only emitted the expected local deployment skip warning.
• Runic v1.7.0 passed over src, test, and docs.
• Checked replacement URLs locally with curl -I -L: raw bench/auto_sweep.jl, raw bench/analyze.jl, and hosted ColPrac docs all returned HTTP 200.