Wall on property boundary

Judging by the excavated material, which is sometimes stored on our property, he has at least dug out to some extent. As mentioned, the street has been at a higher level than his property from the beginning.

I also think that the neighbor has to handle that.

I also think that the neighbor has to take care of it.

I don't quite agree with that!
As it seems, you are in a depression, so lower than the street. Let's say 1.50 meters.
The neighbor digs another 1.50 meters deeper to use the basement, you want 1.50 meters higher from the original ground level. Thus, he has to take care of his excavation, you of your embankment. Thus, you can join forces and each participate half in a common wall.
Nowhere does it say that parking space has to be at street level.
Am I making a mistake in reasoning?

First of all, thank you very much for your efforts! I think it's great!

Here is a graphic for better understanding:



The problem is: Our driveway is where the yellow arrow is. In the northern part, adjacent to the neighboring property, the development plan also provides for parking spaces. Where the red arrow is, the neighbor has dug away the soil down to the basement level.

I don't quite agree with that! It seems you are in a hollow, so lower than the street. Let's say 1.50 meters. The neighbor digs another 1.50 meters deeper to use the basement, you want to be 1.50 meters higher than the original terrain. So he has to deal with his excavation, you with your embankment. Therefore, you can join forces and each participate half in a common wall. Nowhere does it say that parking has to be at street level. Am I making a mistake in reasoning?

Logically, it would be like that. Only then will it become clear to the neighbor internally that with a 3m retaining wall and at worst a 3m garage wall at the property boundary, the basement will become a very dark hole. He will probably want to prevent that with all his might.

Just a general question that partly relates to your concern:
Are there building regulations from the municipality or the state regarding the max. height of a retaining wall?

Example:
In Rhineland-Palatinate, such a wall may be built up to a max. of 1.50 m high – with the neighbor’s consent max. 2.00 m.
If the regulations are similar for you, two retaining walls would have to be built with a small gap in between (or L-shaped stones).
For example, for a total of 3.00 m: 1.50 m wall (L-stone), 0.50 m gap, and another 1.50 m wall (L-stone).