I got myself a valve index, as I've heard that it works well on GNU/Linux (I use Debain 12 with GNOME).
Turns out, there were a bunch of hurtles. At first, my cable was just broken, so I needed to get that relaced. Later on when I got the cable, Everything worked fine, but nothinig is being displayed in the headset. The screen is just off and the frightening red lights on the front are lit. Every time I run steamVR, it doesn't give me any errors, but after about 20 seconds of waiting, these two LEDs turn from blue to red. The eye adjustment slider and even the tracking works perfeclty, as I can see the rendered image in the "VR view":