What we still want to try is to move the house a little towards the northeast, since there is a path running directly along our property on the southwest side and we would only have about 3 meters of distance between our terrace and the path. We are worried that this distance is too small and that one would always feel somewhat observed / overheard.
On the site plan, however, it looks as if the house is already 3 meters away from the right boundary? So nothing more can be done there? Why do you stick the terrace to the left property boundary instead of placing it centered in front of the house? That would be perfect for the afternoon and evening. You don't really need the sun at noon anyway; it is usually too hot. And you can, for example, create an additional breakfast terrace in the top left corner of your property, where the morning sun should shine nicely. You just have to walk a little farther, but there is a tray on which you stack all your stuff. Or alternatively a small breakfast terrace on the southeast side, directly next to the kitchen. The house itself would be quite nice in my opinion, but since the budget is not enough, a new floor plan will probably be needed. It is also important that you furnish the rooms once. For example, in a square bedroom it is difficult to accommodate a separate dressing area. And in the living room, I wonder whether the sofa should then be placed with its back to the hallway or window front so that the TV can go on a wall. I would open the living room much more to the northwest side, place the sofa against the stairwell wall, and give the TV a place on the southwest side; the window there will just have to be a bit smaller. Somehow you are missing the view of the wonderfully large garden; you orient everything towards the side on the narrow strip just because there is southwest.