So, for me it ended up with the local BMW workshop picking up the i4 and bringing it to the workshop.
The cause was a mechanical and electrical defect in the contact/locking pin to the left of the charging socket, and the solution was to replace the contact, the surrounding socket and the charging flap itself. A relatively cheap repair if it should happen outside of warranty, where the costs of the consequences of not being able to charge could easily be much higher than the repair.
The feedback was, that there is no emergency opener for the charging flap on the i4, and also that it is not a common error. In case of it happening in a situation where it is urgent to charge, the recommendation was to force it open, eg. by using an air wedge or a small crowbar. Somewhat of a disappointing design decision to remove the emergency opener; maybe the MTBF is very good on the part, and I just had bad luck?
So, overall a very positive experience with the BMW service response, who also updated the SW, charged and cleaned the car.