If you purchased from Apple even if you signed up for a Carrier installment you will receive a return kit from Apple if you included your wife's iPhone 13 Pro Max. That's how you get the AT&T credits over 36 months. You indicated that you missed that step on Apple.com so you are not setup for the $1000 Carrier Trade-in plan with the monthly Credits.
You posted that you missed that step on Apple.com so you are at the mercy of your near by AT&T Corporate Retail location. Your new 36 month installment will not qualify for device credits. The AT&T Corporate location will need to perform a couple of extra steps. Normally they will only take the Trade-in if you ordered through AT&T.
ETA: bold last sentence.
Dave