Docs: Use a link checker to prevent publishing broken links

### Problem description

As seen in #6550 with PRs #6879 and #6864, there may be content that hyperlinks to things that no longer exist or was moved due to navigation changes. We want to avoid publishing docs with broken links and as we grow the developer content in our docs, it will become harder to constantly check and maintain working hyperlinks.

### Solution description

The solution is to integrate a link checker in our CI using something like https://github.com/UmbrellaDocs/linkspector as part of our check docs workflow.

### Additional context

_No response_