Looking at objects tagged tourism=zoo, aviary is the smallest “zoo type” by far. The second smallest type is zoo=butterfly. (Overpass) I’m not familiar with them so I can’t judge if it’s accurate to describe them as zoos.
There is also zoo=enclosure, this is, according to the Wiki, both used for whole zoos and for invidual enclosures, not in a zoo. An example would be this one where wild boars are kept in the middle of a forest (OSM). I wouldn’t really call that a zoo, and as the history of the object shows, I am not the only one. It could make sense to also discourage this specific use of the tag?
