3-story house required.

You should read through the state building code, also regarding the topic of the definition of a full floor.

but according to the development plan and the building authority's statement, only a house with 3 floors can be built there.

In building law, there are no floors, only full floors. Always pay attention to what the building authority has said and what you assume they have said.

So that means I could possibly manage to build 2 full floors and maybe then designate the attic as the third floor?

If the attic is then a full floor.

How can one tell that the neighbors have not adhered to this?

From the aerial photo.

One last question. How many floors does the house in the attached picture have? Just so I can get some understanding.

A full floor is regulated differently in every federal state. As an example, we roughly take the 2/3 rule: an attic is a full floor if the living area of the attic with a ceiling height from 2.20 m is at least 2/3 of the ground floor. This is related to the slope, but also to the knee wall and dormers: In this case, the roof is very steep, and there are dormers as well. Ultimately, you have to calculate. It is estimated to be 3 full floors.

what exactly does that mean?

Since this point is listed under building design, it IMHO only affects the facade design, meaning that a base projecting in front of the outer wall must not be higher than 30 cm. Here, neither condition is met: the base is higher than 30 cm and exceeds the ground floor height.

How can one tell that the neighbors have not adhered to this?

The roof structures are very clearly visible in the aerial image.

How do you know that there are trees there?

They are also clearly visible in the aerial image. Likewise, that just recently a multi-family house was built two properties away.

How many floors does the house in the attached picture have?

It cannot be clearly determined from the picture. In my opinion, it just narrowly misses being a full floor.

Okay. Really complicated altogether.

Because the roof pitch is probably also prescribed, using the attic as a third floor will probably also be difficult......

Yes, that sounds more like selling to me, I must admit. When I dream of owning a home, it’s definitely not over 3 full floors and not with multiple tenants in my house. But of course, everyone has to know that for themselves.

Creating a full floor is neither more nor less complicated than avoiding a full floor.

A single-family home remains a single-family home, and I would definitely prefer neighbors above or below me compared to the vertical apartment aka terraced house with seven meters of garden "width" - a horizon, as the name suggests, is not portrait orientation.

Impact noise is overrated; even the wildest neighboring children don’t spend their entire childhood jumping and bouncing in the apartment. A view (penthouse) remains a view, and the "bungalow" can have its own entrance and use the stairwell for the upper floors only as a route to the basement.

A multi-family house area remains a multi-family house area - this would not be changed by building only a single apartment on your own property in the middle of it. A garden or penthouse condominium developed on your own is definitely more valuable than just being able to "design" non-load-bearing walls. Having neighbors above or below my bungalow would not be a drama for me. After all, you build a bungalow to have all rooms on one floor, and not primarily because of the skylights.

There might be the option: no basement, but on the ground floor a spacious double garage, house technology and storage room. 1st floor as usual living/dining/cooking/guest and on the 2nd floor the bedrooms. That’s the layout. This might possibly be cheaper than moving everything down one floor and starting with the mentioned layout in the basement. But quite a few people who are restricted to two stories and might be very grateful to be allowed to build three stories without a basement do build like this.