Hello, Welcome to OpenStreetMap.

OSM had the highway tagged as a track, third party apps are to blame for your problems. OSM has not implied that the track is a "public footpath/bridleway/permissive path". Your grievance ought to be taken up with apps that lay false claims about access to your track.

I've amended the tags to access=agricultural, foot=no, highway=track, vehicle=private. I've added the gates at each end as well taging them as access=private, barrier=gate, foot=no, vehicle=private. With this tagging OSM would consider there to be no public access whatever.

Regards Bernard.