There is no development plan and according to the Saxon Building Code, something like that is permit-free up to 2 meters. The neighbors even dug out more three years ago and also did not need a permit for this. Therefore, I assume that we also do not need a permit.
This was told to us by an earthworks company, which in the end is too far away. They also did not make us an offer because of the distance. He only mentioned something about a construction trade license... but after a long internet search I could not find anything concrete about it.