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.
KDE Plasma. I have not tried any other. XFCE is too basic and I hate Gnome. Even if it worked without any problem, I don’t think I could use another DE.
You should try a different one to isolate the problem. Is it something specific to KDE or your system more generally.