https://wiki.openstreetmap.org/wiki/Key:amenity

specifically says 

"Biergarten or beer garden is an open-air area where alcoholic beverages along with food is prepared and served. See also the description of the tags amenity=pub;bar;restaurant. A biergarten can commonly be found attached to a beer hall, pub, bar, or restaurant. In this case, you can use biergarten=yes additional to amenity=pub;bar;restaurant. 

None of this really helps as the important thing about the Beer Garden is availabilit of alcoholic beverages, which the leisure=outdoor_seating
outdoor_seating=garden combination doesn't imply.

I propose the Biergaten tag be changed to encompass the English Beer Gardens instead.