Testing Wayland on Kubuntu 23.10 (dev) on a Macbook, the middle and right touchpad clicks act as normal left click. The settings to do the actions with 2 or 3 fingers work, but actual physical pressing in the middle and to the right of the lower touchpad is unexpectedly the same as pressing to the left, while in X11 I have the expected results.
When you use a MacBook, the Libinput input driver automatically switches into “Clickfinger” mode, which means that to right-click you need to put two fingers on the pad then press down with either of them, or with your thumb. This is the way right-clicking works on macOS. To middle-click, put three fingers on the pad and press with any of them or your thumb.
It’s configurable, though. Find the Touchpad page in System Settings and set “Right-Clicking: Press bottom-right corner” to activate the alternate mode where you right-click by pressing. This switches into “Areas” mode, which is what you were used to on X11.
The reason why this is different for you on X11 vs Wayland is because the settings are stored differently on each for technical reasons. So what’s happening is that your X11-specific setting isn’t being honored on Wayland, so it falls back to the internal default settings of the Libinput driver itself, which is the Clickfinger mode since you have a MacBook.