Heya, the access=private tagging on https://www.openstreetmap.org/way/500401928 was probably correct, and the error there was the missing foot=designated + designation=public_footpath tagging.

access=private sets the default access, which in this case would affect the access for vehicles. foot=designated would then override that for pedestrians.

It looks like a private drive, so I suggest the correct tagging is: access=private + foot=designated + designation=public_footpath.