Many headphones can do audio over usb-c if you want a wired connection. If you want to use a fully analog set of cans, you can also just get a usb-c to 3.5mm adapter for a few bucks.
No need for wireless and battery, just not the plug you were expecting.
If it’s anything like the lightning to 3.5mm adapters I’ll be buying one of those once a month for the rest of my life.