Ah, your initial post had links to source upgrades, hence why I asked. Also you mention updating ruby, etc, which is simply not needed with an omnibus installation, since Gitlab takes care of updating it’s components as and when it’s needed.
Suggest you start here, this link has a ton of resources to look at including the upgrade path - since you will need to follow the upgrade path to ensure a successful upgrade: GitLab Upgrade Path Resources
You do not need to stop Gitlab, if you do this, services required for the upgrade process will not be running, and things like database migrations will not occur. Gitlab will stop any services it needs to stop during the upgrade process. Postgresql is also bundled in the omnibus package, and Gitlab itself will take care of upgrading this when it’s needed.
You also need to make sure background migrations have finished before starting the next upgrade on the upgrade path. If you don’t, and upgrade before they have finished, you will break your Gitlab installation.