Rabbi Michi, I asked explicitly about powers that are independent of the Creator of the world, as distinct from human beings, who operate within a given framework of laws (whether the Creator intervenes or not). People turn to angels so that they will act outside that framework of laws. How does that fit together? Seemingly, angels acting independently are subject to a dispute between the Babylonian Talmud and the Jerusalem Talmud?

I don’t understand what the difference is. Human beings also act outside the laws. Free choice goes beyond the laws of physics. In my opinion there is no difference at all. But even if that were true only of angels, I still don’t see any problem with it. They received powers from the Holy One, blessed be He, to act as they do, and that’s all.

Human beings act outside the laws but are still subject to them; angels have autonomy within their spheres of activity. To the extent that angels received powers from the Holy One, blessed be He, then Judaism is at most based on monolatry, which is one aspect of polytheism, but it is certainly not a monotheistic religion. In monotheism there is no delegation of powers; the one God alone acts (or does not act).
If necessary, I’d be happy to quote direct prayers to angels, such as Metatron, from early literature. Metatron is certainly understood as an independent entity, even if an emanated one.

I don’t understand these hair-splitting arguments. There is no difference at all.
Prayers to angels are an old topic, and there’s no point going over it again.