Thank you both for replying so quick.
I forgot to mention that the previous owner said that the "mechanic" who did the oil change, told him that it is a faulty oil pressure switch.
Given that he has poured 1 extra liter of oil into the engine

, I have my doubts. Maybe he was right...
UPDATE: I did a VCDS check on Module 01 (engine) and there are no DTCs/errors. Tried several times, with only ignition on (oil lamp not flashing) and engine on (flashing oil lamp). No faults in either case. Actually, did a complete scan of all modules and there are no DTCs.
Is it possible that VCDS does not see a faulty oil pressure switch?
Wouldn't I get a DTC/fault in VCDS if the oil pressure were too high or too low in the engine?
Nevertheless, the car has already driven about 500 km without any "weird" engine problems. I hope that I did not screw the engine yet.
I bought a new oil pressure switch today and will post back when I change it (maybe later today). Will also check for "2 oil rings", though cannot imagine that being the issue. The oil cap/filter would just not fit, if there were 2 o-rings on the oil cap stick and top part...
Will update in any event.