The leisure key groups together various different tags for the sake of convenience. There’s no point in looking for any further meaning beyond that. The specific tag leisure=nature_reserve has its own defined meaning, so there’s no issue.
Honestly, if you want to change the meaning of every tag in OSM to fit a dictionary, it might be best if you just started your own map database so you can use whatever definitions you want.
Sigh. At the risk of repeating the same argument yet again, here goes…
Some OSM tags, like “leisure=nature_reserve” are well established and well understood. You need to deal with it and move on - get on with mapping stuff instead of complaining that a tag in OSM isn’t a 100% match for the English word from which it is derived (something that is true for lots of OSM tags - “natural”, “man_made”, “landuse”, etc. etc.).
Perhaps it would help if you thought of OSM’s tags and values as a separate language altogether and not as a variation of English at all? That way you could just use the tag that everyone else uses and wouldn’t see a problem.
For what it’s worth in this particular case I don’t believe that leisure=nature_reserve is in any way a contradiction. I mapped one last week - at no point did I feel annoyed because there were signs preventing human access to meadows used by nesting birds (but a number of hides provided for people to observe them). “leisure” does not mean “I’m allowed to trample anywhere”, even in “English” rather than “OSM”.