On the Bluetooth bit, both Microsoft and Sony don't allow you to use Bluetooth with the Series S/X/PS5; at the very least you need a Bluetooth adapter. Supposedly because the latency in the standard Bluetooth protocol doesn't make for a great experience.
I know that it's a big inconvenience and it's a portable, but it's kind of how things are.
I'd be curious if you could plug an audio device into the USB C port.