Integrate a link validation job

I'm unsure if we could introduce lychee to check links; it might have trouble with Hugo syntax links (eg, `{{< ref "/post/..." >}}`).

Maybe we could generate html from markdown and check the html, though it would make it hard to find where the bad link is used.

No files, tests, or entry points are named. Start by reviewing how this Hugo site generates HTML from Markdown, then evaluate lychee against Hugo reference syntax such as `{{< ref "/post/..." >}}`; the work is done when a link-validation approach is chosen that reports broken links with useful source locations.

Written by the indexing model from the issue text.