If you're on Wayland, there should be a toggle for it in the KDE settings.
For me on Plasma 6, it's called "Middle Click:" and then "Pastes Selected Text", under "Workspace" → "General Behaviour".

If you're on X11, this is implemented in X.org, so X.org would need to provide that option, not KDE. I researched that for half a minute and it didn't look great, but yeah, you'll want to do your own research.
Or try out the Wayland session, if you haven't yet.

Try "keyboard shortcuts" and select some action, then use the button as input, or look in the mouse settings.

Is there a "nothing" action? May be useful here.