only via the correspondence at https://www.openstreetmap.org/changeset/169271037

If a track in a national park has been "closed", and that's indicated I think access=no should apply. access=private makes more sense for something like a driveway that the land owner uses but no one else is permitted to use it. So access=no is stronger, it says no one is allowed to use it. This lines up with how they are documented at https://wiki.openstreetmap.org/wiki/Key:access

Sorry I have no idea about what Alltrails does, but it's up to them how they choose to interpret the tags.

In any case, the lack of a highway=* tag would mean most downstream maps won't display it at all. I suggested to apply abandoned:highway=* instead of having no highway tag at all, so some data consumers who want to specifically check for closed and non-active tracks can still find it.

Mapping these kinds of features is still contentious in OSM and even the current guidance we put together at https://wiki.openstreetmap.org/wiki/Australian_Tagging_Guidelines/Cycling_and_Foot_Paths#Legal_Access isn't universally supported so it's something that can evolve further, but I feel this is a good balance.