Tracking Issue: Unified Astropy Sphinx Theme Migration

I'm opening this issue here to track the work for my [Cycle 5 Proposal](https://github.com/astropy/astropy-project/blob/main/finance/proposal-calls/cycle5/aperio-documentation.md) 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.)

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## 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 - https://github.com/astropy/astropy-sphinx-theme/pull/47
The sphinx-theme repo had got a bit crufty so I gave it a clean up before extending it.~
2. (Postponed to later) *astropy.org website* - Migrate the current website to be hosted on RTD. https://github.com/astropy/astropy.github.com/pull/701 - **Needs someone with astropy.org DNS permissions**
2. ~`astropy-sphinx-theme` New `astropy-unified` theme added - https://github.com/astropy/astropy-sphinx-theme/pull/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. (4a) ~*astropy.org website* - https://github.com/astropy/astropy.github.com/pull/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. (4b) ~`sphinx-astropy` - https://github.com/astropy/sphinx-astropy/pull/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).

1. [ ] Core - https://github.com/astropy/astropy/pull/19206
1. [ ] reproject - https://github.com/astropy/reproject/pull/581
2. [ ] asdf-astropy - https://github.com/astropy/asdf-astropy/pull/325
3. [ ] astropy-healpix - https://github.com/astropy/astropy-healpix/pull/304
4. [ ] astroquery - https://github.com/astropy/astroquery/pull/3590
5. [ ] ccdproc - https://github.com/astropy/ccdproc/pull/922
6. [ ] photutils - https://github.com/astropy/photutils/pull/2274
7. [ ] regions - https://github.com/astropy/regions/pull/664
8. [ ] specreduce - https://github.com/astropy/specreduce/pull/308
9. [ ] specutils - https://github.com/astropy/specutils/pull/1328

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### Other related things

I've opened an issue to discuss learn.astropy.org adopting this: https://github.com/astropy-learn/learn-astropy/issues/140

Start by reading finance/proposal-calls/cycle5/aperio-documentation.md and the Phase 2 checklist in this issue. Then inspect the linked pull requests for Core, reproject, asdf-astropy, and the other coordinated packages. Done means the unified Sphinx theme has been rolled out across the intended packages and the tracking list is complete.

Written by the indexing model from the issue text.