With apple intelligence enabled I am seeing a 10-15 sec delay in push notification. This is actually causing issue with my alarm system, door bells and 2FA requests.
I'm using iPhone 16 Pro. First installed 18.1 Dev beta 5 and AI and noticed this. When beta 6 was released it continued.
I put in FB15389900.
I reported the same issue here:
https://developer.apple.com/forums/thread/764848
For me, updating to the latest iOS 18.1 beta 6 resolved the issue (I am on a iPhone 15 Pro).