You need something like this to convert the optical output on the TV to use with the mixer.

https://smile.amazon.com/ROOFULL-Digital-Converter-Toslink-Optical/dp/B07142SV1D

Then a cable like this to plug it into the mixer

https://smile.amazon.com/Splitter-Smartphone-Computer-Speakers-Amplifier/dp/B0829VWPSB?th=1

Hey. Wanted to share this blog, after TONS of reading about amps/DACs I found that this was the most informative well written blog. If you want to actually learn about why an apple USB C adapter is inadequate scientifically speaking start here. http://nwavguy.blogspot.com/2011/09/more-power.html I'd also recommend you read more about equipment you might purchase at Amir's audio science review.

I personally ended up buying a topping stack E30/L30 for ~250$. I think it was, in the end, a waste of money and a <100$ fiio combo would have done the job, in fact A/B testing with my "audiophile grade gigabyte motherboard" and my 2021 MB pro I couldn't distinguish either of them 90% of the time and it might take me a week to notice if someone swapped the cables under my desk (and volume matched). That being said I don't regret if for a minute because they do for me what no other audio setup had ever done. They just work. Form and function completely nailed. No noise floor, no distortion, no driver issues, extreme volume headroom, and essentially future proof. If you're at all budget limited, I'd buy the nicest amp you can afford (schitt, 02, fiio, JDS, topping) and either the apple USB C (read how well it tests on ASR) or this for the desktop as I felt it was honestly 98% of the topping DAC.

Enjoy your new headphones and I hope you enjoy the source rabbit hole as much as I did!