Can I ride through unoccupied carpark spaces? I got a note from the passing driver for a slow driving over the yellow marked rectangle that means a car is allowed to be parked there. The place is more like a yard but it is also on a bicycle path. There are no any road signs or marking that would explicitly disallow the bicycle traffic there in a way I would understand.

I was not seeing the motorist because he was right behind me.

Should I drive around this marked rectangle or should the driver wait till the place he wants to put a car is free, if multiple bicycles are passing? The location is Switzerland if matters.
AFAIK there are no road rules requiring you to give way to traffic behind you when travelling straight down the road, ie, not turning and not at any intersections.

Riding over an empty carpark space is also completely legal and normal.

There are places where one must not ride more than 2 abreast, and some locations have rules about impeding lane flow, but you're not describing that situation.

You've simply met an impatient driver, not much you can do for them.  Have patience and tolerance.