[ci] add a link-checking job

[jameslamb]

Description

A CI job that catches broken links in documentation should be added here.

Benefits of this work

• avoids link rot (docs) in documentation (especially useful for pages like https://pydistcheck.readthedocs.io/en/latest/how-to-test-a-python-distribution.html with lots of external links)

Acceptance criteria

• a CI job here automatically catches broken links
• that job:
  • does not run as a pre-commit hook
  • does not run on every commit to every pull request
  • runs once a month, some time near the middle of the month
  • can be manually triggered (e.g. via GitHub Actions workflow_dispatch functionality)

Approach

Copying LightGBM's setup would be a good start:

• https://github.com/microsoft/LightGBM/blob/e0c34e7b2f68793bbf46854b85fd750be134446d/.github/workflows/linkchecker.yml
• https://github.com/microsoft/LightGBM/blob/e0c34e7b2f68793bbf46854b85fd750be134446d/docs/.linkcheckerrc
• https://github.com/microsoft/LightGBM/blob/e0c34e7b2f68793bbf46854b85fd750be134446d/.ci/test.sh#L145-L152

But open to other suggestions if someone finding this wants to attempt it!