I can't think of much better options either. So now rather 4m to the neighbor, at least 6m carport, leaving 8m for the house, which I would also be limited in length by the trees and shrubs.
To park two cars side by side and give up that much width... somehow not good either. In the end, a lot will depend on how wide the plot actually is and how far I really have to be from the neighbor...
If things go really well, the plot is 18.30m wide and the distance to the neighbor is 3.50m: Then there would be space of 5.20-5.80 for two parking spaces (depending on the house) - tight but feasible.
If things go really badly, the plot is only 17.70m wide and the distance to the neighbor must be 4m, then there would only be 4.10-4.60 left.
We will see - there will definitely be a solution. I would also prefer it to be 22 meters wide, but it just isn’t. It will be solvable.
Let’s see... at 11.60 house length, maybe the house could be placed with 4m distance to the street - then maybe you could still get a parking space in front of the house, across the width - without any overbuilding. I will also check that.