I see (TIL a lot about CEC, added some info to a sibling comment).
I incidentally found https://hackaday.io/project/168696-cec2usb while poking around, last updated a couple years ago so probably not available for sale anymore, but open source at least.
I've toyed with the idea of replicating its functionality on an Arduino, but ended up just buying the adapter :)
In the end, I'm not sure how doable it is, but it shouldn't be too complex. Licensing is another matter. I'm at a loss as to why GPU makers don't wire it up though.