USB-C headphones need to essentially host the USB controller, some microcontroller to coordinate it all, DAC (Digital to Analog Converter) and a suitable amplif

USB-C headphones need to essentially host the USB controller, some microcontroller to coordinate it all, DAC (Digital to Analog Converter) and a suitable amplifier to drive the actual speakers. And that amplifier very likely needs more than the 5V coming over USB C so you need some sort of DC-DC boost converter that is dead silent and stable so it plays the transients clearly. Getting this all right in such a constrained space is possible, but as all things analog it requires some serious engineering and not just a "we throw that one good chip on and we'll be good". IMO you still fare better by getting decent cans and even a cheap USB soundcard like the Behringer UMC series.