Users not part of the backend team cannot test their Synapse PRs against matching Sytest branches

This issue has been migrated from [#12754](https://github.com/matrix-org/synapse/issues/12754).

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Sytest has a feature where by if you create a Synapse branch and a Sytest branch with the same name, your synapse PR is tested against it. However, this only works if your branch is on `matrix-org/sytest`, **not** a fork.

This leaves anyone who does not have commit access to `sytest` out in the cold regarding this feature, which means it's impossible to make CI pass if you are making changes that require fixing sytest without invoking someone on the team to create a branch on your behalf.

My recommendation would be to make Sytest a bit smarter and to ask GitHub if any PRs have been linked to the Sytest PR ~~(which I believe you can do in GitHub Actions via the API)~~ (nope, will require more thought) and check that out.

No files or tests are named. Start by locating the Sytest CI logic that matches Synapse and Sytest branch names, then review how GitHub PR links or fork branches could be discovered. Done means contributors without matrix-org/sytest access can have matching Sytest branches used to test their Synapse PRs.

Written by the indexing model from the issue text.