… What exactly do you need the Elgato for? All the Elgato does is capture external HDMI signals.
If you had 2 PCs, you would use the Elgato to send the gaming PC’s screen to the streaming PC. If you had an Xbox, you would use it to capture the Xbox’s screen on your PC for streaming.
If you have 1 PC, you don’t need an Elgato, KDE already knows what your PC screen looks like, it is laying it out.
What you should be doing is just “open OBS and set up your scenes and start streaming.” The only thing you might want to do is go into the video settings and set it to use NVENC (I think you can do that on Linux) to offload the encoding to your GPU (which has dedicated encoding hardware) instead of your CPU.
Everything else should just work the same as it does on Windows.
To be clear: The Elgato HD60 X does not do any streaming… it is a video capture device. OBS does all the streaming, and it already has access to all the things it needs to capture by nature of being on the PC. You can just capture your desktop in OBS without the Elgato.