The differential is normal. The lower hose is supposed to stay a lot cooler than the upper hose because it’s the cool side of the system - coming out of the radiator.
As for temps, at 221-223 the t-stat is not quite fully open, so you still have a little cooling capacity left. I would expect your fan to be running pretty hard at that point while idling since you don’t have the airflow from driving - though not absolutely certain. Is the fan running pretty hard? I’d keep an eye on the temps for a while just to make sure you don’t spike up while driving, but I think you’re probably okay.