Hey RBGE!
It's an Ubuntu Server 18.04 with nginx.
I was aware that I need to update PHP in prior. There was a green check when updater checked the installed php-version (installed php8.1).
It seems, that the updater was able to execute one database migration step from it's list (something with v16.x..). After that, 2 migration steps were left (v1.17 oauth2 and one more) where the update stucks.