Add UI tests

[jyn514]

Would have been very helpful to catch #992, #935, the issues from #981.

[Kixiron]

I've actually been looking into this for a while, but it's mostly blocked on full build tests (#822)
There's two real routes, one is traditional programmatic browsers where you write code that emulates a user, and make sure everything does what's expected and the other is via snapshot testing

Programmatic interaction can be very fragile, since it involves a lot of querying css selectors which tend to not like doing what they're told. Most involve containers of some kind, but that also applies to snapshot tests because they need a rendering engine of some sort.
These are a few of the promising libraries I've seen for testing clients, I think thirtyfour is the most promising since it has the most features and seems to be the most widely used. It also has the advantage of being able to take screenshots, so we could potentially get the best of both worlds with being able to interact well with the site while also having resilient tests

• thirtyfour
• fantoccini
• selenium-rs

The second method I've seen is by snapshotting. This can be achieved with thirtyfour (as mentioned above), but @GuillaumeGomez has also been working on a snapshot testing library for rustdoc, but I don't know where in development he is right now

[GuillaumeGomez]

It's useable. What might be missing is what I didn't need until now.