[CI] Publish CHANGELOG and other top-level `*.md` files on the Docsy site and drop `markdown-link-check`

[chalin]

I think that it's useful to have at least the CHANGELOG published to the Docsy website. If we publish all top-level *.md files we'll be able to eliminate the need for the extra link checking via markdown-link-check. We'll then be able to rely on htmltest's reference caching capabilities.

I'm marking this is CI/infrastructure related since this is in part motivated replacing markdown-link-check by use of htmltest.

[chalin]

And here's another reason: CI runs can fail because external link checking is inherently unstable. E.g.:

• https://github.com/google/docsy/actions/runs/7513143585/job/20454576805:

    22 links checked.
    [✖] https://badges.netlify.com/api/docsydocs.svg?branch=main → Status: 0
  Error: Process completed with exit code 123.
  

• https://github.com/google/docsy/actions/runs/7515766717/job/20460078471