I can provide a partial answer in regards to the Bluetooth concerns.
In regards to Bluetooth:
Be sure to keep an eye open for "Apt-X LL" codec support on both the headset and the PC. It does make a huge difference for latency over Bluetooth. With a good USB adapter or built-in Bluetooth on the PC, it will open the door to using any Apt-X LL headset you may be interested in.
I would recommend the Creative BT-W3 for an adapter.
This device works like a USB sound card for the PC (or Android, game console, etc.) and handles the Bluetooth devices natively in the adapter.
You may also find some gaming headsets that support both Bluetooth and have their own USB wireless dongle. This adapter may still be useful as a 2nd dongle to bring your headset around to multiple devices or possibly even stream both devices at the same time.