Hi Cyrille37,
I am always happy to communicate with you. The "surface=ground" has already been added to the street. It will serve your purpose.
I believe that the road classification should be "highway=track" and added in this relation: https://www.openstreetmap.org/relation/1827491 a "highway=primary" tag so that users can recognize this track as part of a primary-rated relationship, with the proposed=primary tag removed. I think this is the best way to represent it. If you have another perspective, please share it with me.
Best regards,
nona mostafa