When plugging them in with 3.5mm on either PS5's controller or directly on Switch they immediately work (which means they default to 2ch rather than 7.1/3D on devices that don't support it) regardless if I previously disconnect the USB cable from PC or still had it plugged in - AUX port takes priority in an instant, meaning that they always work by power or draining battery and switch modes no matter what I had on PC just a second before.
I tried again with USB and still nothing. I also tried with the USB-C>USB-C cable for the first time. On PS5 a "Too many USB devices at once" notifications pops up when using the USB-C port there, Headset isn't detected. On Switch in portable mode using the USB-C port the headset isn't detected either, not that I expected it to, only 3.5mm jack works - actually connecting both at the same time produces a "tick" sound every second or so, and removing the USB-C cable solves that. Interesting glitch.