Neighbor wants to take over setback areas - experiences

The construction as planned, in my opinion, you will not be able to prevent. Your missing signature on the plan will at most only cost time. However, this has nothing to do with the [Abstandsflaechenuebernahme]. You did not sign that.

I admittedly did not understand the matter and also did not know that hobby rooms and saunas are allowed to be built on the boundary.

It is not allowed because they are living spaces, and of course this applies on both sides.

Unfortunately @Escroda is actually missing here he could tell us whether the clearance area can possibly be mutually transferred.

a) yes and b) you do not need him for that, logic already says that this cannot be the case: the same area can only serve one clearance elimination at the same time (that is why it only works into public ways up to their middle).