surface is a secondary tag : we use a primary tag, telling that the area is a residential, an industrial, a road and then you add a tag surface (see wiki https://wiki.openstreetmap.org/wiki/Key:surface : "additional information").
So you cannot use only the tag surface, we have to find the main tag.

Because of your pictures, I was thinking there was a construction project here. But I understand that I confused because of the panels with the roadwork.

Do you think the result of the area (with a lot of mud/ground) is because of the roadwork ? If yes, I mean if the area was with grass before the roadwork, probably the grass will come back at spring if the roadwork is finished. So natural=grassland will be ok even if now it doen't fit well (I see a panel "private land" so I imagine nobody will stand on this area and grass will probably come back).