My 13 Pro Max came from AT&T with a nano-SIM preinstalled. I did the setup/transfer, but the 13 didn't show any service and my old 11 Pro Max still worked and received calls. I tried using the transfer cellular plan to eSIM on the 13, but ultimately kept getting an "OOPS!" screen from AT&T.
Wound up moving my old SIM card to the 13, removing the new one that didn't seem to be doing anything. Problem with that was, no 5G support with the old SIM. The old SIM only listed LTE and 4G choices.
Wasted more time trying to figure out what to do. Went to my account on att.com and tried the Activate a device, and it listed my 13 with the new SIM number, so I put that back in, and chose activate. After a minute, I toggled Airplane mode and the new SIM then showed service. I went into SETTINGS/Cellular/Cellular Data Options, and finally saw "5G Auto" for the Voice & Data setting.
So swapping SIM's does work, but if your old SIM is a 4G/LTE SIM, you won't get 5G in the new phone (AT&T at least).