dev: include the HTML documentation build in the local lint suite

[kumarUjjawal]

Which issue does this PR close?

• Part of Add Local Scripts to Reproduce Full CI #21048.

Rationale for this change

./dev/rust_lint.sh runs the non-functional CI checks locally, but not the
documentation website build. Sphinx builds with -W, so one warning fails CI.
A contributor sees that failure only after a push.

What changes are included in this PR?

• ci/scripts/check_docs_html.sh runs the existing docs/build.sh through uv.
  It works from any directory. It reports a missing uv, cargo,
  cargo-depgraph, dot, or make before the build starts, and installs
  nothing. It has no write mode.
• dev/rust_lint.sh runs the new script as a read-only step.
• The "Test doc build" job runs the same script. The path filters of the job
  also watch the script.
• docs/source/contributor-guide/testing.md documents the command.

docs/build.sh still owns the Sphinx and dependency-graph commands. The Python
dependencies and the Sphinx settings do not change.

What is the testing strategy for this PR?

Local checks with command stubs and a real build:

• The script starts the same build from the repository root and from other
  directories.
• -h, --help, --write, --allow-dirty, and an unknown flag all fail
  before any tool runs.
• Each missing tool gives one message and a non-zero exit.
• Failures in uv, cargo depgraph, and dot keep their exit code.
• A real build writes docs/build/html/index.html and changes no tracked file.
• One Sphinx warning, a page outside every toctree, fails the build.

uv run ./dev/rust_lint.sh passes with the new step.

Are there any user-facing changes?

No. This changes the contributor tooling only.

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 82.45%. Comparing base (0576a0b) to head (9452e63).
⚠️ Report is 24 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #25586      +/-   ##
==========================================
+ Coverage   82.42%   82.45%   +0.02%     
==========================================
  Files        1139     1140       +1     
  Lines      435372   436589    +1217     
  Branches   435372   436589    +1217     
==========================================
+ Hits       358845   359979    +1134     
- Misses      54826    54849      +23     
- Partials    21701    21761      +60     

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[2010YOUY01]

Tested it locally and it's 👌🏼 . Thank you.

[2010YOUY01]

Small optional advice, we can do it after finishing all scripts.

This testing.md is an entry-point documentation for testing, so I think we don't have to explain all non-functional tests in detail. The detailed documentation could go to individual scripts.

Maybe it's enough to list all of them, and briefly introduce them in 1-2 sentences here.

[kumarUjjawal]

sounds good! I will open a new pr after all of the scripts are merged.

[kumarUjjawal]

Thank you @2010YOUY01 for the review