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).
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