[CI] Running `/fix:cmd` over a PR rebuilds but skips GH action checks

[chalin]

For context, see:

• #4335

Unless we get a separate bot to handle /fix:* commands, we're stuck with this behavior: GH doesn't rerun actions if a workflow over the same repo committed a change to a PR. I usually work around this by forcing a change (via rebase, or by making a trivial edit) over the PR, but that isn't always practical.

Other possible solutions:

• Create a separate bot to handle /fix:* commands so that GH runs the full action checks. (This would be a lot of work but might be worth it in the long run.)
• Run a cron job that rebuilds the site after changes are made to the main branch. (This is easier to setup, and will at least notify us if build checks are broken).

Thoughts @open-telemetry/docs-maintainers?