Restore and migrate GitLab
Restore the latest backup of the GitLab database to the new instance, and migrate GitLab to use the new cloudsql proxy service.
While it would be possible to try a transparent migration by simply repointing the existing service to the new cloudsql proxy deployment, that's probably a bad idea. It would require all services to move at the same time, and DB upgrades aren't exactly transparent so it's safer to go one-at-a-time, and make rollback easy.