Link checking in CI

[swiatekm]

Describe the issue you're reporting

When and how should we check links in the CI? Our current check is completely nonfunctional, so I'm disabling it in #3424. I tried to fix it, but couldn't get markdown-link-check to not report a bunch of false positives.

Roughly what we should aim for in my opinion:

• Broken links introduced in a PR should be caught by the CI run for that PR
• Broken links in the changelog should be caught by the release PR CI
• We should periodically check all the links in all of our markdown documents (how often? where do we report failures?)

There's also the question of what tool to use here. markdown-link-check seems to produce a lot of false positives, so maybe we should try https://github.com/UmbrellaDocs/linkspector instead?