How Could God Be Perfect If He Regrets Something He Did?

Questions about how God could be perfect if he regrets something he did, whether there’s a difference between God’s sovereignty and God’s providence, and what Nehemiah meant when he said God “put it into his heart” to do certain things. Does Genesis 6:6 mean God made a mistake since it says he regretted that he had made humans? How could God be perfect if he regrets something he did? Is there a difference between God’s sovereignty and God’s providence? When Nehemiah says in 2:12 and 7:5 that God “put it into his heart” to do certain things, is this just another way of describing God’s guidance?