release: update patch process
Created by: bobheadxi
This has fallen pretty out of sync with the release template, updates to try and align better with the new tooling. Some adjustments made require tooling updates: https://github.com/sourcegraph/sourcegraph/pull/15548
Also adds steps for requesting patches: https://github.com/sourcegraph/sourcegraph/pull/15550
Closes https://github.com/sourcegraph/sourcegraph/issues/15293