Currently, poetry collections are tagged as fiction/nonfiction in addition to poetry. Fiction and nonfiction are prose genres, distinct from poetry; poetry is neither fiction nor nonfiction.
Personally, this means I don't really track my poetry on the app, as it messes up my stats for fiction and nonfiction.
This also means that works of literary criticism have their genre marked as poetry. In other words, both a collection of poems and a work of prose literary criticism can be marked as nonfiction poetry.
The same also applies for drama pieces. Shakespeare was not a fiction writer; he was a playwright: he wrote neither short stories nor novels; he wrote plays/drama. That should be reflected by the genre when you have read a play.
This would also make for deeper accuracy in the stats and allow better tracking.