pavucontrol(1)only showed one output; "Dummy".
After looking at the latest packages in
/var/cache/apt/archives/, I didn't really get any bright ideas of what could be the cause.
I tried booting some older kernels, to see if that was the problem. Still no sound.
The fact that even older kernels didn't have sound any more made me think of the updating of initramfs's when a kernel package is updated. Maybe something went wrong there?
sudo update-initramfs -k all -c and reboot later, and sound works again. Phew.