M1 Max 16". Recently updated to Monterey 12.6.3, and upon upgrading, many internal trackpad gestures stopped working: three-finger tap/click, four-finger tap/click, all the tip-taps, etc. Oddly, the three-finger click-swipes still work. Checked in live view and no clicks are registered when I do any of these gestures. Can confirm that this is BTT-related, as three-finger taps/click still work with MiddleClick. BTT version is 4.008 (2222), latest available alpha version.
Maybe it's not the gestures that don't work but the actions?
Monterey has been quite buggy in regards to permissions. As a first step I'd try to remove BTT from System Preferences => Security & Privacy => Privacy => Accessibility and then add it again manually. (Quit BTT before doing this).
Apple has improved this a lot on Ventura, is there a reason you need to stay on Monterey?