The standard install is the only officially supported way of installing but you can find information on restoring a backup below. It should be the same process for a DO 1-Click install.
It looks like the 1-Click app is explicitly using Ubuntu 20.04 so until that changes, it’s probably worth staying on 20.04. It’ll continue getting bug fix / security updates for another three years so there’s no rush to move to 22.04.
You may as well try reinstalling Docker first though. Perhaps the problem emerged from the upgrade and conceivably the Docker networking being removed, then re-added by the install could fix it.