Ok guys, I have an update. Since I've had a working backup of Mojave on my internal HDD, I finally caved and did the following:
1. Booted the backup Mojave HDD (created by Carbon Copy Cloner)
2. Wiped clean the NVME drive with the failed Catalina update
3. Created a Catalina Install USB drive
4. Installed a clean Catalina on the NVME main drive
5. Migrated the settings and home folder from my backed-up Mojave HDD to the newly installed Catalina drive
Voila, it worked. I have a working Catalina macOS main drive with working sound, USB, ethernet etc.
Only thing not working is Sidecar (dont know why), but I can live with that.
What went wrong the first time? Don't know, but I suspect, that it must have been something with the system files / permissions etc., therefore a "migration" was not going to work. Anyway, I'm happy it's okay now and I encourage all of you to update this way. Make a clean Catalina drive and then migrate your old Mojave home folders etc.