But we are going around in circles here: You won’t get certainty by buying and submitting the building application. You only have certainty once it is approved or you go and talk to them.
It’s not that simple. There is also the state building code.
The plot is already bought, if I understood correctly. So politely asking now helps little.
The problem is probably more that an architect/draftsperson authorized to draw would knowingly violate the state building code with the knowledge of a theoretical setback obligation. The question remains how this "offense" is assessed and whether anyone will go along with it.
Strictly speaking, the building application would probably have to be submitted to the building authority with the information about the neighbor’s illegal construction including its removal. That leads exactly to what the OP didn’t want. A huge fuss.
Therefore, I stick to my point. Just submit the building application and pretend you know nothing. Otherwise, prepare for a long processing time with a neighborhood dispute. That will probably get uglier and more expensive than putting aside sum x for a possible fine.