Just to check: were you using OsmAnd+’s vehicle routing mode, or its pedestrian routing mode? I just tried with pedestrian routing mode and it plotted the route along this path fine.

It looks like an oversight that the other part was not also marked as access=private. I’ve fixed that, thanks.

I’m not sure what you mean by Track #143420491. Could you link to it please? (Right-click on the map and choose ‘Query features’.)