During seliḥot, we* interweave saying piyyuṭim with the recitation of the 13 middot. This is thematically sensible, since the recitation of the 13 middot is supposed to effect God's forgiveness1 2, and the piyyuṭim are also on the topic of asking for mercy/forgiveness.
What is this relationship? Why does the recitation of the 13 middot require a piyyuṭ? What is the earliest source for such a relationship, and are there contrary opinions?
*Based on Artscroll and Koren Ashkenazi siddurim/machzorim, and Daniel Goldschmidt's machzorim/seliḥot.