If you get an unlocked phone, by fully paying the price up front, you should be able to put in a SIM or even get the carrier to provision an eSIM with the existing number.
Yeah I don't know if buying through AT&T can avoid those notifications. Maybe there are account settings to disable or block those.
But if your'e willing to pay the full price up front, then no reason to buy through AT&T unless your local stores have them in stock while nearest Apple stores may not.
I moved from iPhone 12 to 13 Pro Max. I had a T-Mobile eSIM. When I set up my new phone, I transferred all the data and settings from the old to the new iPhone through short-range wireless transfer. As part of this transfer process, the new iPhone detected the eSIM in the old iPhone and asked if I wanted to transfer it. I tapped yes and it just happened.
Got an email from T-Mobile saying my account had been transferred from IMSI number x to IMSI number y.