I have more problems telling Linux to not play audio through my dualsense controller

Open pavucontrol, go to the "Configuration" tab, and for that device profile, choose "Off".

You could also just select something else as default device in the "Output Devices" tab, but disabling the device will keep it entirely off the list of options, if you don't want it used.

I tend to do that with the HDMI outputs on my video cards as these days video cards can stream audio to televisions via HDMI and the like, and I never want to actually use my monitor as an audio output device; I have dedicated, discrete speakers.