This just shows the natural=wood / landuse=forest tags are a bit useless IMO.
The landuse is not necessarily related to what’s on the ground (ie the landcover). I think it would be better to just have one tag for any area (mostly) covered by trees, whether it is “natural” or not. Then use additional tags to describe whether it is managed, and what it is used for etc.

I would suggest just having a tag for something like natural=trees, for any area (mostly) covered by trees, and depreciating the tags for natural=wood / landuse=forest / landuse=wood.