Hi, welcome to OpenStreetMap and thanks for updating Nashes Farm Lane.

The original highway=unclassified tag doesn't imply anything about the usability of the road. It fits on the hierarchy of roads at about the same level as highway=residential. From the definitions in the OSM wiki (links below), this does not look  like it should be highway=tertiary.

You could add surface=asphalt to the road, as the surface is currently untagged. There's also smoothness=*, but that's more of a subjective tag.

I hope that's useful. If you would like any help, please don't hesitate to ask.

https://wiki.openstreetmap.org/wiki/Tag:highway%3Dunclassified
https://wiki.openstreetmap.org/wiki/Tag:highway%3Dtertiary
https://wiki.openstreetmap.org/wiki/Tag:surface%3Dasphalt
https://wiki.openstreetmap.org/wiki/Key:smoothness