The answer will, of course, vary depending on religion and even depending on sect or school of thought within the same religion, but here’s the Sunni Islamic answer as I understand it: God has emotions befitting of His grace and perfection, as opposed to our imperfect human emotions. For example a human might get angry and say or do something that they regret, but God’s anger doesn’t take away from His wisdom (I think Christianity has something about God regretting flooding the Earth in Noah’s time, but islam rejects that sort of thing out of principle). God’s mercy doesn’t make Him commit injustice, as a human might. Etc etc. We humans don’t need a deeper understanding of Allah than this, so Islam doesn’t really get into the details of these things, but that’s the gist of it. This does contradict your premise that God should be beyond emotion, but there’s really no reason for that to be the case. God should obviously be beyond imperfection, but emotions aren’t inherently imperfection; only humans’ flawed emotions are.