Thank you for the additional documents. I also agree with the architects' opinion. Reference height is 155.77 m + 5m * 2% = 155.87 finished floor level.
With the eaves height and ridge height, almost everything works here.
Since you are building with a basement, you probably also have some leftover material that you can use for filling.
I would talk to the neighbor to allow him to do the filling up to your property with a slope of 2:1. He has the advantage that he can build the garage. And you save fill material.
Check whether a CP is allowed closer to the street. Otherwise, you have the same problem on the path as your neighbor to the south.