As discussed in #11408:
* Improve documentation for the release process.
* Fix the description for the PRs created by the `prepare release pr` workflow.
* Fix pushing tag in the `deploy` workflow.
* Build the package only once, and test on all platforms.
* Deploy is now triggered manually via an Action, which is then responsible for tagging the repository after the package has been uploaded successfully.
* Drop 'docs': we nowadays rely on readthedocs preview PR builds.
I still think it makes sense to always serve docs from the release branch (rather than the latest tagged release), but that means we need to update it on new releases.
The docs already assume an 'upstream' remote, so we can only fetch from there instead of fetching all remotes. We also don't need to hardcode the remote URL.