We unfortunately had to withdraw from our contract because we had problems with the architect assigned to us.
What is an "assigned architect"? – that sounds like in an East German restaurant where the waiter seats you even though all seats are free ;-)
We are only allowed to build flush with the street, however, both neighboring houses do not stand directly on the boundary.
I would see a violation of the principle of proportionality here in interpreting the concept of flushness obviously contrary to reality as "precisely" a few centimeters. An extension to the line of – I suspect – the courtyard wall would seem sufficient to meet the flushness requirement. I also see an obligation to extend here only on one side, and due to lack of clarity also your free choice whether to build adjoining 280/1 or 283.
We would like to clarify beforehand how to deal with the resulting gap
Such cases used to occur regularly, and the gaps were then closed with a board (since mice get through, always also passable for cats).
and whether a prefabricated house with wooden frame construction would even be feasible.
I assume their salespeople will boastfully say yes, but from my point of view no. Timber frame construction is possible, but fully prefabricated and just erected on site, no. Without at least partial on-site construction, I don’t see anything that can be fit precisely enough – neither the buildings nor the boundary concerned. Have you researched why the plot (at least according to the drawing: currently) is free from development? Check out there is a hint on how you can tell me more privately...