Thought I would add my story here, as my trade in went really smooth.
On Sept 17, I pre-ordered the iPhone 13 Pro Max for in-store pick up on Sept 24, with a trade in of my iPhone 12 Pro Max valued at $790. Picked up my new phone at the Apple store with no issues on Sept 24. Received the trade in kit on Sept 29. Went to UPS on Saturday morning, Oct 2, and dropped it off (made sure to weigh package and get receipt, which I immediately took a picture of in the UPS store).
Apple received the box yesterday, Oct 6, and today, Oct 7, sent an email that my trade in was complete and I will be issued the $790 refund in 5 days.
I'm very happy to say that the process was really easy!