Should we burninate poetry, and if not, how should we use this tag?
Following the guideline from Meta.SE on burninating, I'd say keep it.
Does it describe the contents of the questions to which it is applied? and is it unambiguous?
Yes, poetry is a clearly defined area of literature.
Is the concept described even on-topic for the site?
I very much think so.
Does the tag add any meaningful information to the post?
I'd agree here too.
Does it mean the same thing in all common contexts?
Haven't checked since we are already at 3 checks for keeping it.
Should we burninate poetry? No. At least, not right now.
It is true that a books tag would be be redundant, but then poems, like novels, are often printed in books. I have a stack of them sitting beside me, waiting to be read (or re-read).
I would certainly use poetry as one of my favourite tags, so that I could find poetry questions of interest to me, so I think that such a tag would be useful. If we find that it is little-used, then we can burninate it.