This tutorial shows how to enable touchpad 4-finger swipe and pinch gestures in Ubuntu 24.04 and 24.10 with default GNOME Desktop on Wayland.
GNOME since version 40 supports 3-finger swipe gestures to switch between workspaces and trigger overview screen. And, there’s an extension Gesture Improvements to enhance the features with 4-finger and pinch gestures support. However, the extension only supports Gnome from version 40 to 44.
If you want to extend the gestures on recent GNOME 45 ~ 47 (meaning Ubuntu 24.04, Ubuntu 24.10, Fedora Workstation 40-42, etc), there’s now an open-source fork to do the job on Wayland.