Implement link checking workflow

Part of #45. Implement a link checking workflow, that checks for broken links on a page. Ideally the tool only runs on the changed page in a PR (to safe time and prevent positives on files unrelated to the PR) but is also able to check the full site - ideally not statically but served via our own express app.

As mentioned in #45, the problem spans wider than just broken links: we also want to make sure every page we generate is also discoverable (say linked, see https://github.com/GoogleChrome/developer.chrome.com/issues/83) on the site and we also want to make sure our external sources are not broken.

- [ ] Start a product requirements doc (PRD), evaluating and documenting possible existing tools and their pros/cons (https://github.com/untitaker/hyperlink, https://github.com/lycheeverse/lychee, ...) with the goals mentioned above in mind
- [ ] Implement the checking logic in this repo (for example as a gulp task)
- [ ] Add task as a workflow to d.c.c
- [ ] Add task as a workflow to web.dev
- [ ] Fix existing broken links