If you want to trade in an old phone without doing it at the time you purchase a new one, the only way to receive the trade in value is via an Apple gift card.
I was looking forward to getting $160 gift card for my old iPhone 11 but after reading all this I think I’ll just leave it in a drawer.
Not so. I just traded in/upgraded (on a Verizon contract, but AT the Apple Store; maybe that affects this… but still paying Apple directly) and they handed me the new phone and had FedEx send a trade-in mailer that I had a while to send back with my trade-in.
If you sell it directly to another human, or even use something like ebay, you'll get more and they'll pay less.