I'm not a headset gamer guy so I haven't looked into it that much, but I doubt any conventional bluetooth headphone would be very good latency wise; you'd probably need a latency-optimized protocol (that would likely not be stellar quality-wise). There's AptX LL but it seems pretty poorly supported.

Wonder if anyone makes analog RF transmitter dongles/recievers you can plug wired headphones into? Cursory googling doesn't find much.