I believe you might want to double check your phone and/or headphones. Or even the Deck itself.
I use it daily and apart from the expected latency, the audio is great with no flaws. No interruptions or jank.
Bluetooth 4.0 is capable of handling around 8 connections simultaneously
To be fair, cheating on a MMO is very different from cheating on a precision FPS game.
If you do pixel perfect inputs on a MMO it barely matters. If you do pixel perfect inputs on a FPS you can win an international tournament.
VRR works really well already - some Nvidia users might lose extra functionality like Reflex Ultra that, when paired with VRR, can smartly adjust the frame rate cap. But VRR itself works.
HDR is a difficult beast though... It's hard even on Windows, and very problematic on Linux (though with Gamescope, KDE Plasma and Wayland you can kinda use it already).
Bluetooth headphones work well with the Steam Deck, I specially like how you can pair your phone to the Deck and it will mix the phone's audio with the game audio (so you can have music or a podcast playing, for instance)
For those asking how to do it, simply enable Bluetooth on the phone and then go to the Steam Deck's Bluetooth page, find the phone and pair it from there.
Bluetooth controllers actually do behave weirdly on the Deck, the polling rate is sub optimal. You can modify certain system files to help, but you'd have to reset the setting after every update.
But for audio, it's mostly fine. I really do not have issues using this phone to Deck setup. You could consider a full system reset if it's that bad on your end, it's supposed to work well.