Add a version picker UI to the documentation website

[matrixbot]

This issue has been migrated from #11647.

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The documentation for each Synapse version is stored in each version's respective directory under the gh-pages branch of this repository: https://github.com/matrix-org/synapse/tree/gh-pages. There are additionally develop and latest directories which contain the very latest build of the documentation, and the documentation of the most recent, stable Synapse release respectively.

Currently, individual versions of this documentation is only accessible by navigating to it directly by URL, e.g https://matrix-org.github.io/synapse/v1.40.

Ideally, it would be possible to switch between versions via a button in the website's UI. The website currently lacks such UI.

We can build something from scratch, like what was done for the custom table of contents sidebar: https://github.com/matrix-org/synapse/blob/develop/docs/website_files/README.md

An example of a version switcher that could be used with a little tweaking is the one that can be seen in NixOS' documentation: https://nixos.org/manual/nix/stable/. The JS source for which is available at: https://github.com/NixOS/nixos-homepage/blob/c4a3ed90fbea5386e4060a3f3f623d52b99c9ec4/js/manual-version-switch.js. However, this sort of UI may become unruly when we have 100 different versions of Synapse to sift through, so ideally something that can be scrolled/paginated would be used.

[dklimpel]

IMO this was fixed by:

• Adding a version picker for Synapse docs matrix-org/synapse#16533