Open design - semi-detached house without neighbors?

The development plan says "Single-family house or semi-detached house is allowed"

To avoid misunderstandings regarding the terms:
Colloquial language:
Single-family house = single-family house
Semi-detached house = semi-detached house
Planning law (§22 Building Use Ordinance and 3.1, 3.1.4 Plan Sign Ordinance):
o = open construction method
ED = only single and semi-detached houses permitted

He brings someone else in and they build a semi-detached house (connected by a thick wall).

If the plot is not actually divided, it is colloquially a semi-detached house, but in planning law it is a single house consisting of two residential buildings.

The neighbor on plot B must - since it is open construction - maintain a minimum distance to plot A.

No, he does not have to, at least not because of the open construction (see §22, paragraph 2 Building Use Ordinance). If he submits his building application to the approval authority before the neighbor, he can build on the boundary. However, he then needs a building encumbrance, which the neighbor can refuse.

And the OP is free to choose on plot A

No. If both his neighbors built with boundary distances - for which they do not need a building encumbrance - he can no longer build a semi-detached house, because then he must also comply with boundary distances.

Many thanks in advance for the numerous responses!

Maybe I need to present my thoughts more clearly:

I want to build a detached single-family house. But since semi-detached houses are also allowed with the open construction method, I wonder if it can happen that the neighbor, if he was earlier, has already built a semi-detached house on the property boundary to mine.

Thanks a lot in advance for the numerous responses!

Maybe I need to explain my thoughts better once again:

I want to build a detached single-family house.
However, since semi-detached houses are also allowed with the open construction method, I wonder if it could happen that the neighbor, if they acted earlier, has already built a semi-detached house on the plot boundary to my property.

Just show the plot of land. So far, quite a few confusing things have been written here.

For example, with a plot of 700 sqm, it is more likely to be understood that you can either build a single-family house on it (with a setback from the neighbor) or two semi-detached houses, meaning two houses each with its own entrance, and each then having 350 sqm of land.

whether it can happen to me that the neighbor, if he was ahead, has already built a semi-detached house on the property boundary towards me.

If he has already built, you can see whether the house is on the boundary. If there is no house yet, you should check the register of encumbrances and the land register before you buy. If your desired plot is not encumbered, the neighbor is not allowed to build on the boundary. For safety, you can also inquire at the approval authority whether something has already been submitted. The seller should know this as well.