Hi, I don’t know what app you’re using to route, but it’s the app which is at fault here, not the previous access tagging.

The foot=designated tag should override access=private to allow foot routing. access=private sets the defaults, and is needed to ensure that the track is not considered as a public road for vehicles.

See https://wiki.openstreetmap.org/wiki/Key:access#Road_where_residents,_pedestrians_and_cyclists_are_allowed