Thanks for your help and suggestions!
When it wasn’t possible to update the firmware via Digitest, I was about to give up, so i just left the unit powered on while doing other things. After an hour or so, I heard the fans slowing down an then the displays and diods lit up. I was able to update the FW and after a reboot it seemed to work - Pro Tools recognized the HD Omni and the meters on the interface were indicating signal, but there was no sound from any outputs (TRS, D-Sub or headphones).
After another restart of the Omni, Mac and PT though, everything seems to work again.
