Is border construction over 9 meters allowed in Saxony?

With us, the neighbors had to sign the building application plans because we also built directly on the boundary. One copy for the office, one for the builder, and one for the neighbor.

In Saxony, a garage (should also apply to carports) is exempt from approval if the floor area is less than (or equal to) 50 m² and the average height is < 3m. Therefore, we do not have a building permit application for it.
At best, an informal written confirmation from all parties involved with a sketch would be sufficient.
Alternatively, the garden house would then simply have to maintain a 3m distance from the boundary and I can position it at will, right?

I, Egon, and all my legal successors agree. That means whoever buys from Egon also buys his consent

That is exactly what the land register ensures, that knowledge about this also definitely reaches Egon's property buyers.