Heya, is it definitely this whole path which is closed off? The northern segment of it was marked as a public footpath, so it seems a bit odd (although definitely not impossible) that it would be closed for conservation reasons rather than being fixed/improved.

In any case, it’s quite possible that someone may come along and re-add the paths in future, from sources such as MapThePaths or Strava Heatmap. To avoid that happening, the recommendation* is to retag closed paths as disused:highway=footway rather than highway=footway, and add a note= explaining why the path is closed. That way, if someone comes to re-add the path in future they’ll see it’s already there and is explicitly closed.

* See https://wiki.openstreetmap.org/wiki/Talk:Organised_Editing/Activities/National_Trust_Paths#Closed_routes_(e.g._for_safety)

Does that fit in with what you surveyed on the ground?

Thanks!