Upgrading HA NextCloud servers

We are currently running NextCloud 13 on two web servers in a high-availability configuration, and are looking to upgrade using the command-line built-in updater (https://docs.nextcloud.com/server/20/admin_manual/maintenance/update.html#).

Will the built-in updater upgrade both of our servers, or does it need to be run on each server independently? Will the upgrade process work on the second server if the upgrade of the first server made changes to the NextCloud database? Alternatively, should we upgrade one server using the built-in updater then copy the nextcloud directory over to the other server?

Should we be using the manual upgrade steps (https://docs.nextcloud.com/server/20/admin_manual/maintenance/manual_upgrade.html) instead? If so, should both servers be stopped before the upgrade, or can one server stay online while the other is upgraded (and then we swap)?