^I’d say rap is a either a form of poetry or a maybe sui generis form of performance art, but it is not music. Like theater, cinema, and dance, rap uses music but is not music.
I think it is significant that there is a stronger expectation that rappers write their own material. It is perfectly acceptable for a professional singer to reinterpret old standards, but rappers who merely perform what others have written are looked down upon by other rappers and rap aficionados(?) (or so I’ve heard). That says to me that rap is more of a verbal art than musical one—hence, I’m more inclined to call it poetry than music.