I don't understand pulseaudio. Should I use JACK? Does every application support JACK?

It's OK. You're not alone. No one understands the Linux audio stack

My Pulseaudio sets my NVIDIA Card's HDMI card to the highest priority. Now if I start OBS or Cava it automatically selects the HDMI Output, although I set my Logitech G533 as Default Output. Makes no sense to me

You can use a pulseaudio to jack module for the applications that absolutely need pulseaudio. It's called pulseaudio jack sink.

I personally like pulseaudio a lot.

I use it with the KDE-Integration, pactl and pavcontrol and some custom shell scripts to:

- Record in background with a null sink.
- Record only certain apps while hearing others too with the LADSPA-module. (e.g. hear Spotify while playing & recording a game)
- Former, TS-Bot with a second TS3-Instance. (Before Discord came)

... and lots more like that. You can just get very creative with the programs and modules mentioned above.

Pulse audio was the biggest entry barrier for me. Lol.