It would be nice if we have a rebase button next to the update base branch (which merges master to this branch). I usually prefer the rebase because it helps to keep the commit history cleaner.

This isn't possible via the API. Even merging only recently became possible: https://developer.github.com/v3/pulls/#update-a-pull-request-branch
I don't think the API offers _any_ such destructive options (_rebase_ rewrites history and thus it requires --force)
For anyone that wants this, there is a GitHub action that does it:
https://github.com/cirrus-actions/rebase
If anyone wants to build an extension for this, it's possible but you'll need a third-party server to clone and force push (which is basically what that action does on GitHub鈥檚 own Action servers)
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This isn't possible via the API. Even merging only recently became possible: https://developer.github.com/v3/pulls/#update-a-pull-request-branch
I don't think the API offers _any_ such destructive options (_rebase_ rewrites history and thus it requires
--force)