You can do this already by accessing bluetooth through an app such as Open Room VR, but it comes at the cost of certain games having horrible performance drops, Beat Saber being one of them.
( If someone publish an application on the store that trigger the bluetooth setting.
It is already implemented in the Quest. It is just not accessible. )
The command to use is:
adb shell am start -a android.settings.BLUETOOTH_SETTINGS
Bluetooth = latency. aptx low latency (if Quest supports it) will be <50ms. But most normal BT headsets introduce 100-300 ms of lag. Which is really bad for VR and rythm games.
This seems to have been added with the latest 7.0 release for Quest - I was able to connect my bluetooth headphones via the 'experimental' settings option although they can remove these settings at anytime
Latency is the main problem. Bluetooth 5 has lower latency compared to BT 4, but I don't think the Quest has BT 5 with the 835 SOC, otherwise Oculus probably would've included the wireless option.
I don't really see the point in wireless headphones when your ears are mere centimeters from the jacks. It just introduces latency, reduced fidelity, more radio clutter and the inconvenience of having to charge them.