Actually it could really be my bad (*): I must have (unintentionally?) re-assigned some mouse button (I can’t remember right now why I might have done that, but doesn’t matter).
In any case, I had a “Mouse Profile”, which is different from the “Default” (sic!) profile! So switching back to the “Default” profile gave me the following assignments:
That looks much better now.
So in case anyone else is running into this: check your “mouse profile” and you might need to switch back to the “Default” profile (and restart with custom assignments from there, as needed)!
UPDATE: Thinking about it some more this is my bad - sorry about the fuss! But could still be helpful for others who fall into the same pit.