I had some kind of hardware lockup, thus a forced reboot (ctrl-syrq+s/u/s/b) and the end result was that /var/lib/xcp/state.db was corrupted and xapi was not starting. I ended deleting that file to have it automatically recreated empty/from scratch, and restoring all my VMs from backup.
Since then, all my Xen Orchestra installations cannot connect to the (VNC) console of the VMs running on this host; it works on the same XOA for another host that is in another pool, so the problem is probably not on XOA but on on the XCP-NG host.
I'm not sure by what mechanism XOA connects to VNC (how it connects to the Unix socket /var/run/xen/vnc-N from what is a remote machine), so if anybody has a hint how I can debug this?
Connecting to the VNC console by redirecting /var/run/xen/vnc-N (where N is the domid) to a TCP port and connecting to that TCP port still works, so the VNC console itself works.