Hey again,
it only took another night of sleep and some further research to solve my issue... so everything is working fine now. Sorry for apparently not doing enough research before asking questions.
Everybody having the same issues with their Taranis connected via USB to their Linux machine may want to take a look at the openTX wiki on GitHub: https://github.com/opentx/opentx/wiki/OpenTX-USB-J...
According to this wiki page, the joystick driver by default adds some dead zone to the sticks around their center position. In my case, running "jscal -c /dev/input/js0" and recalibrating the Taranis within Linux did the trick and removed the dead zones.
All the best,
Stefan
PS: Keep up the great work! Also big thanks for supporting Linux.