If I understand you correctly, you are trying to plug the jack into Phone or Steam Deck and USBc into your headset. I would guess, that your research was kind of right and the cables you tried are the other way round: USBc to Jack and not Jack to USBc.
For Jack to USBc you can e.g. use this cable: https://shop.fairphone.com/de/shop/fairbuds-xl-headphones-usb-c-mini-jack-3-5mm-cable-64?category=5