Turns out that yes we do (Of course! :-)): leisure=garden + garden:type=green_wall, used 22 times, but also another 38 “facade_garden”, which may be the same thing?
It’s not really a garden you can walk through, so I would advise against leisure=garden in general here.
I suggest inventing a new tag (see ATYL on the Wiki) and not diversifying leisure=garden even more than the status quo.
This is the correct tagging and green_wall already implies that it is a way and not a node or area (well, it is an area of course but this would be micromapping on the “insane” level imho) so I would not hesitate to use it on a way.
for sure it is but “green wall” is an established term and I would go for it.