I would do that too. However, if you have 6 meters to the east, turning the cars including conventional carport supports might be a bit problematic.
I would rather say that from the view out of the house you then get a wider angle view also to the left (SE) into the garden ;)
But wait and see: every orientation has something to add value to a garden. In terribly hot weather, you will be sitting on a bench on the north side in front of the front door and enjoying yourselves there :D Cozy seating areas can never be enough and enhance a garden.
I would move the house in the north as close to the neighbor as possible (I believe 2.5m minimum distance), that is enough for a walkway to the door.
In the west, there would then be space for a driveway/parking space, certainly something more than 2.5m but only what is minimally necessary to comfortably park the car and do some maneuvering. Are there any tips here on how to best plan something like this, i.e., how much space does a car need to "park and unpark"? Is it better to plan the parking spot aligned with the driveway (west→east) or to park around the corner (car orientation = north→south)?
In this constellation, the garden would be used to the maximum in the south and as much as possible in the east despite the parking space. In the west, besides the parking space and the outdoor unit of the heat pump, I don’t see much garden left.