Tracking Issue: Unified Astropy Sphinx Theme Migration

[Cadair]

I'm opening this issue here to track the work for my Cycle 5 Proposal across the various packages in the Astropy ecosystem.

I won't duplicate the proposal document here, as that gives a high level overview of the work.

A personal plea: I don't have many hours for this project, so I'm trying to keep the scope tight. I'd really appreciate it if reviewers bear this in mind, if I spend all the time tweaking small things then this project wont get finished. (I'm 66% of the way through my time.)

---

Phase 1

Theme Development & Website

The first phase of this work is now mostly complete, this involved converting the astropy.org website into a sphinx project and adding the new theme to the astropy-sphinx-theme repo.

PRs for this work are now up for review, the following is the intended merge order, ones marked as draft are not ready for review but the others are now ready for review.

1. astropy-sphinx-theme cleanup - Repo Cleanup astropy-sphinx-theme#47
   The sphinx-theme repo had got a bit crufty so I gave it a clean up before extending it.
2. astropy-sphinx-theme New astropy-unified theme added - Add New Astropy Theme astropy-sphinx-theme#48
   This is the place to comment on the visuals of the theme and also astropy specific settings such as the content of the header and footer etc.
3. (3a) astropy.org website - Rewrite to a sphinx project and use unified theme astropy.github.com#698
   This PR is ready to review, all be it not merge (it needs the theme PR). When reviewing this PR theme comments should be left on the theme PR.
4. (3b) sphinx-astropy - Add a new confv3 with astropy-unified theme sphinx-astropy#94
   This PR adds a v3 config which enables the new theme, this can be merged independently of the website PR (as it does not use sphinx-astropy).

Phase 2

Roll out to all coordinated packages (and any others who want it).

I'll open a bunch of these PRs soon to assist in reviewing the theme PR.

1. reproject - WIP: Test out new astropy theme reproject#581
   This is a demo PR to assist in reviewing the theme PR.
2. Core - Test out new unified theme astropy#19206

---

Other related things

I've opened an issue to discuss learn.astropy.org adopting this: astropy-learn/learn-astropy#140