First of all, thank you for posting such an inspirational project! We did two versions as you can see in the renderings, first one is with garage doors that are in dark grey, and wood panels on ground floor next to garage doors. The second version has wooden furnishing of the garage doors and is without wooden panels as you will see.
On first floor there is a perforated metal structure- mask, it is functioning as both aesthetic as well as shade, and you will see horizontal rectangular plant pots that are on some of a parts of this metal structure, on the places that are reachable when opening the doors on the first floor, because of the watering of the plants and for easy grooming. The metal structure is connected to the wall by steel load bearing structure.
The garage dimensions are 5.6 meters in depth and the wall of the garage is pushed at maximum lenght and is placed just below where the drainage canal is showed in dwg. Also, on the right side of the structure we added small room for storage where there were the walls that formed the fence prior ( if that structure is not possible to be build - it doen't affect the project). On the fist floor we placed the storage room as you asked, and room with gym and bathroom with jaccuzzi. Gym has space for tree medium sized training machines ( stationary bike, rowing machine, treadmill and weight bench) or for two large training machines ( large treadmill, combination training machine, etc.).
We hope you will like our project, and of course we would be glad to do more of consulting if you choose our proposition.