I did a little digging. Apparently there's a bug on Meta's end where the left eye is copied to the right, causing flicker, up through v81. It might be that. This is apparently entirely limited to Passthrough/Link sessions, and could be fixed by switching to the Compatibility+ pipeline... but I can't do that during the vote (can't update it), and it really sounds like something they're trying to fix. Are you just using WebXR, or have you tried the download?
Apparently the most recent version, which appears to be in the clear, is v83; but I have no idea just how new-slash-broken that version might be. Hope you get it working!
ADDENDUM: Apparently they still haven't figured out if it's a software thing or a hardware thing, but some users have gotten around it by switching to SteamVR as the OpenXR runtime, which does not have that issue.