Unfortunately "something has gone seriously wrong" is pretty much a useless message. You can boot into a live image to and chroot into the system to fix or chase whatever it is. Its not for the faint of heart though. You would need to check the log files which should be in /var/log. Check the snap and apt logs. Then try to go from there. That being said once you are live booted into a chroot you should have no trouble accessing your personal data. From there you can back it up and do whatever is the easiest method for you. While Linux theoretically shouldn't need to reinstalled pretty much ever sometimes it's the quickest and easiest way to go about it. It just depends on how much damage was done. And again.. that message is pretty useless.
My personal suggestion is to backup your data first from a live image. Then once you chroot in maybe try an from the chroot and see if it does a bunch of stuff, this will likely (not guaranteed) get you a bootable system as the update just functions with the apt command. It sounds like packages just never successfully configured. Only a guess though.
For the chroot I recommend mounting your temp style directories into the chroot as so. Learned this from Arch wiki. $CHROOT being wherever you have the system mounted at.
Code:
for i in sys dev run ; do
sudo mount --make-rslave --rbind /"$i" /"$CHROOT"/"$i"
done
sudo mount --bind -t proc /proc /"$CHROOT"/proc
This should eliminate any troubles with needing these directories for package installation and it will think it's actually booted with a fully functional system behind it.
