The wiki says this about landuse:grass: 

"A tag for a smaller areas of mown and managed grass for example in the middle of a roundabout, verges beside a road or in the middle of a dual carriageway."

That would not seem to apply here. It would not make sense to tag the entire Botanic Gardens with landuse:grass (it is not a smaller area, and it is not entirely grass), and it would not make sense to make many multiple smaller areas of landuse:grass. 

Closing this comment.