Oh, looks like I am able to use the text console to login. I remembered that Virtual Machine Manager (VMM) offered a serial console connection, opened it and found the familiar TTY login prompt. Oddly enough, the “Ubuntu Core” boot splash keeps spinning the spinner and says “Starting recovery system…” on the virt-viewer display all the while.
Does that increase my chances of fixing this manually, @ogra? I’m really one for fixing problems, rather than nuking them. 
But I’m also curious, why the desktop won’t come up. systemctl status graphical.target says it’s running, though.
BTW, I now know what causes this:
Apparently, @paddylandau’s Virtualbox setup does not include/enable a serial console; toyed with some VMM settings and, in the process, accidentally deleted the respective serial device. After that the newly booted VM kept spamming its journal with that message.