But this way we take more space from the garden towards the back.
This is not comprehensible to me: The garage is 7 meters away from the north side.
If you move it as edge development to the north, you do get a slightly larger driveway and roughly one meter "less" garden somewhere in the south, but honestly, one should very gladly, very very gladly give that up if you get a light-flooded house and can even open the house to the west. West is much more important in summer; south is important for the interior rooms in the O-O months. Additionally, a garden appears larger if you can also look at it diagonally. Ultimately, if you look at the "backyard development," a bit more courtyard area can’t be wrong either. Visually, a (right) angle always appears positive (this lever was also applied for the terrace).