Switch documentation theme to Furo

[pradyunsg]

Follow up to #8420

[nicoddemus]

Thanks a lot @pradyunsg for following up with this!

I have a few comments, enumerating them for easy reference:

1. The docs build failed because of some warnings... do you know if the theme can affect those @pradyunsg ?

2. In https://pytest--9788.org.readthedocs.build/en/9788/reference/reference.html, I see this warning:

3. The topics on the left side contain too much information initially, for example:

I would expect less topics, because the API reference, changelog, etc are all buried all the way down on the scroll... is that something we can adjust by reorganizing the files a bit?

[pradyunsg]

1. Yea, I'm not sure what the fix for that is. It's related to the Sphinx upgrade to 4.3.x, rather than the theme.
2. Yup, and that's mostly a matter of removing the .. contents:: from those page sources.
3. Yes, we can. We'd need to introduce a page for that, so I'd probably add an "How To Guides" page, that has all the relevant how to pages "under" it. (see the sidebar in https://pradyunsg.me/furo and the reference section or the contributing section)

[pradyunsg]

I've excluded Sphinx 4.4, since it added an additional check for extlinks that... I don't want to deal with cleaning up to be honest.

And, yes, I'll split this into a bunch of sensible commits. I just wanted to whip something up quickly to make sure I don't drop the ball on this immediately after picking it back up. :)

[pradyunsg]

Closing in favour of #12326.