Then mir-kiosk is not running which would explain why client snaps fail to work.
That is probably because mir-kiosk tries to start and fails, the logs may tell us why. You should be able to VT switch (Ctrl-Alt-F1) to the greeter and log in normally. If that fails ssh in from another machine and disable the daemon:
sudo snap set mir-kiosk daemon=false
Both Ubuntu Desktop and Ubuntu Server are “classic” systems, as are Fedora, Arch etc. the distinction snapd makes is between “core” (i.e. Ubuntu Core) and “classic” systems.