They have diplomatic relations with the Cardassian Empire and Gul Ducat is a representative of them. If they arrested him it would have immediate diplomatic implications. Ultimately the only way to stop the Cardassians or the Klingons is via war or a more protracted diplomatic and cultural approach.We were actively at war with them and we dont have the Prime Directive either. I dont see the feds arresting Gul Ducat whenever he steps into Fed jurisdiction
They have no diplomatic relations with the Mirror Universe. They know that Georgiou was responsible for multiple acts of genocide, torture, slavery and cannibalism (which can be attested via computer records and direct witness testimony).
To put it another way, if you found a man on a desert island atop the corpses of the thousands he had killed, tortured and eaten, would you say "Nope, we don't have jurisdiction"? If you would, you would be failing justice.
Just as another point universal jurisdiction is not restricted to the Nazis, you can read the wikipedia page if you'd like to learn more about how, in the real world, it is applied: