How does E-Sim transfer work during Apple iPhone trade in?

That information is incorrect. The new phone has to be setup before the trade-in of the old device. If you use Quick Start, that can be done in the store normally and when that is done and you activate your phone, it will take you through transferring the eSIM from the old phone to the new one. Once the new phone is setup, the old phone is wiped and turned over.

I had a similar query, and I contacted Apple Support (India). You will have to factory reset and hand over your phone to the delivery agent. The diagnostic test would be done after that. Therefore, you would not get an opportunity to transfer your eSim. You will have to contact the service provider for transferring your eSim. It is very unfortunate that apple has to trouble its customers opting for trade in, when a very simple change in procedure can save us a lot of trouble.

@akshithb1908, can you please confirm here if you went through with this and what was your actual experience? This is a very common problem and I know that in store they do have support for this but if you opt-in for a home delivery I am not sure. It also depends on country to country as I remember seeing for Apple Australia, people get 2 weeks to ship the old product back to apple.