I recently bought a 2022 Yukon AT4 from Mississippi and shipped it here to California. This was just last month (March). It had a factory Cat-back exhaust as one of the options on it. Both the dealer and I were both worried about it passing California emissions because of where it was, but everything worked out just fine. I just needed to get it smogged. The taxes and licenses were paid in Mississippi when I made the purchase. There were no internal mechanical systems in the engine that were any different than here in California, or lack thereof, so you should be good.
The only thing out of the ordinary that I had to do was put miles on it. I know it sounds crazy, but when I received the vehicle, it only had 13 miles on it. It's kind of an oxy moron to drive it illegally, but that's what it takes. The oxygen sensor hadn't quite yet matured yet, so it wasn't registering as it should. I burned in 500 miles, and it worked just fine after that. So it cleared smog, the DMV did their visual inspection, and I got my license plates that same day.
As for that dealership, I call BS.