Led bulbs don’t draw anything like the current of a filament bulb therefore it is possible that the sensing of the switch simply isn’t seeing it. My boat is a 2007 B42 and I have replaced all bulbs with LED and haven’t had this happen but I know it can, might be worth checking the various connections through the wiring.
Re the fridge question, I believe the fridge is switched through a relay at the top of the panel which may well be faulty, the relays can be unplugged from the panel and replaced.
As a general electrical point Bavaria use a bus bar as a common point of contact for a number of the negative feeds. On this bus bar are two (sometimes more) multipoint plugs well worth disconnecting them and checking for over heating and certainly that they are all making good connections.