Add action to detect broken links

[ValerianRey]

It would be nice to be able to automatically detect broken links in the built documentation, README, and in the code (in comments, docstrings, and maybe even in strings). There are probably existing tools for this.

[PierreQuinton]

Using make linkcheck from the docs repo seems to do exactly that, for instance it detected two broken links, one 404 and one 403.

[ValerianRey]

Is there a way to detect broken links in README too? What about comments in the code?

[PierreQuinton]

Yes, there is:

- name: Link Checker
        uses: lycheeverse/lychee-action@v1.9.0
        with:
          # Arguments to pass to lychee
          args: --verbose --no-progress "README.md" "CONTRIBUTING.md"
          # Fail the action if broken links are found
          fail: true

Can I try that in the the tests job, right before the build doc? Arguably, these tests need to be run only once, not on all machines/versions.