Opinions?
You have no opinion on my post #13?
However, parking is not allowed on this street anyway
That is not the reason for rejection, but rather the "maintenance of safety and smoothness of traffic." It probably means that additional turning traffic would hinder the flow of traffic and create another source of danger. Whether this is a sufficient balancing for the discretionary decision can ultimately only be clarified by a court.
IMHO, your legal claim to the development of your property through the existing access road is fulfilled. Another access would be a special use under §18 StrWG, the approval of which is at the discretion of the authority. Here, your individual interest must be balanced against public interests. I cannot recognize this balancing process in the official letter. If parking is not allowed on the street according to the StVO, you can formulate a very detailed written weighing of interests yourself instead of the authority (relief of parking pressure, avoidance of parking search traffic, increase in safety through fewer illegally parked vehicles, minimization of the increase in sealed areas, equal treatment like the neighborhood, ...) and address a higher hierarchical level – the last consequence being a lawsuit.
Or you submit a building application for a garage.
Or you ask the neighbor if you may share his access (requirement: very good neighborly relationship).