Move Flutter SDK release process to CI

We used to have a local script to automate the release process. But now we are restricted from direct pushing to master branch. We need to change the workflow to accommodate the new restrictions.

Start by locating the local script that currently automates the Flutter SDK release and the repository's existing CI configuration. Trace the steps that require direct pushes to master, then move the release flow into CI so it works with the branch restrictions; done means the SDK can be released without direct master pushes.

Written by the indexing model from the issue text.