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* Bump peaceiris/actions-gh-pages from 3.9.2 to 3.9.3

Bumps [peaceiris/actions-gh-pages](https://github.com/peaceiris/actions-gh-pages) from 3.9.2 to 3.9.3.
- [Release notes](https://github.com/peaceiris/actions-gh-pages/releases)
- [Changelog](https://github.com/peaceiris/actions-gh-pages/blob/main/CHANGELOG.md)
- [Commits](https://github.com/peaceiris/actions-gh-pages/compare/bd8c6b06eba6b3d25d72b7a1767993c0aeee42e7...373f7f263a76c20808c831209c920827a82a2847

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Signed-off-by: Sean Quah <seanq@matrix.org>

Add developer documentation for the Federation Sender and add a documentation mechanism using Sphinx. (#15265)

Co-authored-by: Patrick Cloke <clokep@users.noreply.github.com>

* Bump peaceiris/actions-gh-pages from 3.9.1 to 3.9.2

Bumps [peaceiris/actions-gh-pages](https://github.com/peaceiris/actions-gh-pages) from 3.9.1 to 3.9.2.
- [Release notes](https://github.com/peaceiris/actions-gh-pages/releases)
- [Changelog](https://github.com/peaceiris/actions-gh-pages/blob/main/CHANGELOG.md)
- [Commits](https://github.com/peaceiris/actions-gh-pages/compare/64b46b4226a4a12da2239ba3ea5aa73e3163c75b...bd8c6b06eba6b3d25d72b7a1767993c0aeee42e7

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* Bump peaceiris/actions-gh-pages from 3.9.0 to 3.9.1

Bumps [peaceiris/actions-gh-pages](https://github.com/peaceiris/actions-gh-pages) from 3.9.0 to 3.9.1.
- [Release notes](https://github.com/peaceiris/actions-gh-pages/releases)
- [Changelog](https://github.com/peaceiris/actions-gh-pages/blob/main/CHANGELOG.md)
- [Commits](https://github.com/peaceiris/actions-gh-pages/compare/de7ea6f8efb354206b205ef54722213d99067935...64b46b4226a4a12da2239ba3ea5aa73e3163c75b

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* Bump actions/checkout from 2 to 3

Bumps [actions/checkout](https://github.com/actions/checkout) from 2 to 3.
- [Release notes](https://github.com/actions/checkout/releases)
- [Changelog](https://github.com/actions/checkout/blob/main/CHANGELOG.md)
- [Commits](https://github.com/actions/checkout/compare/v2...v3

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Co-authored-by: David Robertson <davidr@element.io>

Update mdbook (the tool used to render the documentation website) to version 0.4.17.

This should fix stale deleted files being still accessible.

Currently when a new build of the docs is created, an `index.html` file does not exist. Typically this would be generated from a`docs/README.md` file - which we have - however we're currently using [docs/README.md](https://github.com/matrix-org/synapse/blob/394673055db4df49bfd58c2f6118834a6d928563/docs/README.md) to explain the docs and point to the website. It is not part of the content of the website. So we end up not having an `index.html` file, which will result in a 404 page if one tries to navigate to `https://matrix-org.github.io/synapse/<docs_version>/index.html`.

This isn't a really problem for the default version of the documentation (currently `develop`), as [navigating to the top-level root](https://matrix-org.github.io/synapse/) of the website (without specifying a version) will [redirect](https://github.com/matrix-org/synapse/blob/a77e6925f26597958eccf0ef9956cb13c536e57e/index.html#L2) you to the Welcome and Overview page of the `develop` docs version.

However, ideally once we add a GUI for switching between versions, we'll want to send the user to `matrix-org.github.io/synapse/<version>/index.html`, which currently isn't generated.

This PR modifies the CI that builds the docs to simply copy the rendered [Welcome & Overview page](https://matrix-org.github.io/synapse/develop/welcome_and_overview.html) to `index.html`.

This PR will run a new "Deploy release-specific documentation" job whenever a push to a branch name matching `release-v*` occurs. Doing so will create/add to a folder named `vX.Y` on the `gh-pages` branch. Doing so will allow us to build up `major.minor` releases of the docs as we release Synapse.

This is especially useful for having a mechanism for keeping around documentation of old/removed features (for those running older versions of Synapse), without needing to clutter the latest copy of the docs.

After a [discussion](https://matrix.to/#/!XaqDhxuTIlvldquJaV:matrix.org/$rKmkBmQle8OwTlGcoyu0BkcWXdnHW3_oap8BMgclwIY?via=matrix.org&via=vector.modular.im&via=envs.net) in #synapse-dev, we wanted to use tags to trigger the documentation deployments, which I agreed with. However, I soon realised that the bash-foo required to turn a tag of `v1.2.3rc1` into `1.2` was a lot more complex than the branch's `release-v1.2`. So, I've gone with the latter for simplicity.

In the future we'll have some UI on the website to switch between versions, but for now you can simply just change 'develop' to 'v1.2' in the URL.