ci(release): Move to getsentry/publish for releases (#775)

A copy of getsentry/sentry#22657 with fixes included.

That said this one is a bit different. We used to use the extra option no-merge when publishing to keep the release branches and also keep master on nightly versions. If we want to keep this, we need to add per-project overrides to getsentry/publish which would increase complexity at this early stage for this fringe case. Instead, I opted to follow what getsentry/sentry does: merge but then immediately after that update the version.