When I think of audiophiles what comes to mind is wood walls, floor and ceiling, acoustic panels, subwoofers, high end speakers and lossless sound formats. I don't use headphones in VR because headphones simply aren't comparable to well calibrated surround sound filling a room.
However sometimes I have no choice and use my open back Sennheiser headphones. Stereo since all those spatial nonsense only messes up the sound imo. They're not bad at simulating bass, but of course you still can't feel it. Anyway $60 budget won't cut it.
Eurogamer did just praise the new XBox headset
The Xbox Wireless Headset is here, Microsoft's first official audio accessory for the Series X and Series S, and it's fantastic. The £90/$100 headset packs in an astonishing amount of features and quality for its relatively affordable price tag, and it may be one of the only first-party headsets for any system that I'd actually recommend.
It's a bit over you price range, but seems like a great deal and good investment. The cool thing is that you can mix two wireless audio sources, listen to your own music while playing games.