I use Arch Linux. When I connect an external monitor to my ThinkPad, the cursor moves erratically on the touchpad. It moves slowly, stutters, doesn’t go where I want it to, or goes past the target. There’s no problem with the mouse. The touchpad doesn’t always cause problems—it happens sometimes, and it’s very frustrating.
idk if it makes a difference but if you deactivate the laptop screen by just closing the lid i’d check if the behavior persists when you fully switch over to “only use external display” in “display configuration” (not on arch atm so they might be labelled slightly differently)
oh and if you still have the option it’d be worth checking if the problem is the same under x11 instead of wayland (might require manual installation)