I would probably have oriented myself with the house on the northern property boundary and positioned the carport on the boundary there. The house docked to it. I see the left side of the house as the living and kitchen side, on the right, i.e. the east, more the other rooms such as the utility room.
As the carport is planned now, it would also be an option for a nice garden, but here too I see the orientation of the house to the west. What comes into play here is that in the months when the sun sets more in the southwest, i.e. the winter months, one does not have the sun for well-being in the rooms. The consequences (lack of light, incandescent light) are not exactly positive for health.
I view your approach critically – sun/warmth are important for the mind. If it becomes too much, one should use sun protection like roller shutters. I see a terrace in the southwest area as optimal.
Best regards in brief