I think an example of music poetry is the song “champagne problems” by Taylor Swift from her evermore album. The whole album has a calmer tone than her other albums because I think the songs are more about processing different problems. “Champagne problems” for example, paints a picture of someone trying to deal with a loss but being conflicted about it, how much help they should get, etc.
In the beginning of the song, she sings,
Your mom's ring in your pocket My picture in your wallet Your heart was glass, I dropped it
I think the last line is similar to a metaphor or simile because she is comparing her someones heart to something she can/did shatter. The line helps get introduced to the problem and how she feels responsible for part of it. Another line say,
And soon they'll have the nerve to deck the halls
That we once walked through
She is referring to ex friends in this verse, but I think it can be related to more than that. I don’t know if she is using a specific poetic device, but the clever wording shows how much the situation impacted her, even if we don’t know what it’s about exactly. The deck the halls lyric sounds like poetry to me. Finally, the last verse of the song says-
You won't remember all my
I think that this is a very powerful last line because even though it doesn’t use much figurative language or poetic devices the simplicity of it after such a powerful complicated song stands out. I think it shows that after all the experience and thoughts the person just went through, it can still be put into another perspective and invalidated in a way. I think that’s also why this song goes through a lot of complications that come with loss and how you can tell how conflicted the person is.
Overall, lyrics that portray this deep of a message and story can easily be compared to the way poetry communicates different themes.