Let's have a look
OpenStreetMap has both roads as highway=tertiary, surface=dirt https://www.openstreetmap.org/way/364758018 https://www.openstreetmap.org/way/364758017
Surface=dirt has this fitting example photo in the documentation https://wiki.openstreetmap.org/wiki/File:Transportation_in_T... (linked on https://wiki.openstreetmap.org/wiki/Key:surface)
I'd argue it should be highway=track https://wiki.openstreetmap.org/wiki/Tag:highway%3Dtrack with possible smoothness=bad https://wiki.openstreetmap.org/wiki/Key:smoothness but it's always tricky depending on country.
