Hey everyone,
I get that using headphones with MiSTer is kinda complicated (optical audio, dac etc), but is it even theoretically possible to get audio from xbox series controller's 3.5 jack, fro instance (or DS4/Dualsense)? The transmission protocol seems proprietary, but can official xbox usb adapter solve that?
Getting audio from MiSTer isn't difficult at all; especially if you have an IO board. If you want to use bluetooth audio, there are 3.5mm to bluetooth transmitters but there will be latency, this is unavoidable, even with codecs like APT-X LL etc. There are also 2.4GHz headsets but again YMMV.
But no, you can't get audio from those controller jacks and you've already answered your own question. The protocols to do so are proprietary and even with an adapter that acts as a USB audio device on the host (like the Xbox USB Adapter), the DE10-Nano can't use it. You could reverse engineer these protocols and use additional hardware to inject the audio signal but you'd still need a convoluted chain of hardware that will inevitably introduce audio latency. So tldr is; you can't do this over USB/Bluetooth via the DE10-Nano natively and you could probably do it with a lot of effort and mess of discrete hardware but it almost certainly isn't worth it and inevitably will exhibit the trade-offs above.
Pick up a pair of Sennheiser 2.4 GHz wireless headphones and plug them into the headphone jack.