Introduce a test that checks for broken links in the HTML docs
I've noticed a couple of broken links in the HTML docs recently (#24674 (closed) and #24151 (closed)). It's been pure chance that I've caught these and it would've been easily possible for a release to go out with this breakage.
This made me wonder whether we could catch these automatically. It looks like there's a bunch of tooling to do this already. It also seems relatively easy to write something like this from scratch.
I feel like adding a CI job to do this would be a nice newcomer project