I know my answer is a bit late, but the "swipe between pages" event is apparently still not supported with Catalyst, which is quite annoying as a conversion from the swipe gesture on iOS from the trackpad swipe gesture on macOS doesn't seem to complicated for Apple to implement natively. And this "swipe between pages" gesture is soooo convenient on macOS. I filed a feedback FB9817972, and encourage you to do the same to have it finally implemented...
mat1696
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Do you know if that’s fixed with Monterey ? I have the same issue with my iMac (plus nightshift not responding after 2 nights sleep) on 11.6.1…