Hello @Gnobelix and thanks again to @firstdefence!
Today I've tried it again. Removed every bit of the driver I could find. Deinstalled, removed files. And re-installed. I got an error message "c windows syswow 64 wintab32 deletefile didn't work code 5". I searched for the solution and got the advice to remove the file manually. And oh wonder - it worked! Eventually this was the error and I got the new driver installed without any further errors. Tried it with Affinity photo and: the pen reacts. So awesome, it finally worked.
Thanks for your advice and for taking the time! You helped a lot!