Garage: design possibility of the roof, appearance

Of course, you are not allowed to build the roof surfaces over the neighbor's property. The issue of boundary construction applies to all properties.

Logically, the roof overhang is built-up area, otherwise a carport of any size could be built.

The specifications you have on the plan are certainly eaves height (EH) and ridge height (RH).
So it has nothing to do with the garage.

For us, the length of the boundary development was fixed at max 9m, the roof overhang should be included in that.
In addition, the floor area ratio is regulated. Here, the garage initially counts fully with its floor area. However, there are apparently special regulations for the garage allowing the floor area ratio to be exceeded accordingly.