I tried booting Proxmox and Ubuntu. Both were crashing instantly on startup.
But after lots of trial and error I finally found the culprit: The Mellanox ConnectX-2 MNPH29C-XTR is seemingly causing the problem. It was working perfectly before. Now, how a BIOS/microcode update is causing this, I don't know.
I might try to update the firmware on the card. That will require some setup since the process is not straightforward. But for now I am happy that I can boot.