Neighbor stores excavated soil on our property

if someone is already making such a fuss,

From my point of view, the fuss is being made by the neighbor (or the companies commissioned by him), because they store their stuff on someone else's property. Without asking.

I would try to talk to the contractors/tradesmen/construction workers why they are using the neighbor's property. Were they instructed to act this way or did they simply do it? Were there any instructions at all? See what happens afterwards...

Regarding the building permit, I would inspect at the building authority what was approved (front house or back house, building window). Afterwards, I would consider how to proceed.

In bw you are also asked! We were allowed to inspect the documents and had 2 weeks to file an objection. Since the neighbor built during the notification procedure and adhered to all boundaries, it was not an issue.

What surprises me is why you have no contact with the neighbor, there must be an address of the responsible construction manager, etc. at the red or green point.

If there is no development plan, the neighbors must be involved in Thuringia just the same, and conversely, if there is a development plan (and it is adhered to), in Bavaria not either.

I also find the behavior of the neighboring builder completely inappropriate. You just don't use someone else's property like that without asking. You simply don't do that. Horrible attitude.
In addition, it seems he is building outside the zoning plan. I wouldn't be surprised if he is doing this without approval. Such types can be found everywhere in Germany, thinking, I'll just create facts, then if necessary I'll pay a fine and have things the way I want. Report immediately to the building authority. Don't waste any time! The more factual it becomes, the harder it is to undo. The building authority certainly did not approve such a deviation from the zoning plan without involving you. I don't believe that.
Here in the development area, someone also had to destroy their foundation slab and start over. Hamburger SUV driver, older age. .... Probably thought the rules don't apply to him. Karsten

As if the neighbor is responsible for the behavior of the BU... no.
Your neighbor certainly doesn't know anything about the customs in construction either.
Here it is completely common practice to temporarily store something across the boundary, even if it is morally and legally not correct. But it doesn't hurt anyone nor do you have a disadvantage.
Basically, you should always think in both directions - he is probably a stranger to you as well?

Brief regards

Here in the construction area, someone also had to destroy their foundation slab and start over. Hamburg SUV driver, older age. .... Probably thought the rules don't apply to him. Karsten

Civil servant... all clear Worked today? Oh... stupid question..