It was already tagged correctly, by you, 10 years ago. Deleting the highway tag in order to hide it from the map is essentially vandalism. I've restored that and removed the redundant access tags.

No pedestrian routing software will send people down a highway=footway + foot=private way, unless the software is hopelessly broken.

If locals are using it as a shortcut because the gate at the S end is unlocked, attempting to remove or hide the path will not help.

https://wiki.openstreetmap.org/wiki/Why_we_won%27t_delete_roads_on_private_property
