eSim card transfer

That depends on the carrier. Some will transfer plans during setup, some will require you to contact the carrier and manually switching and reloading the plan.

Transfer or convert your current SIM to an eSIM on your new iPhone - Apple Support

Last time I did an upgrade with AT&T involved, they needed to be contacted and there was a transfer fee.

But you’ll see what the current migration status is when you perform the iPhone migration, as you’ll either get the automatic cellular plan transfer sequence shown, or you’ll need to contact the carrier; AT&T.

AT&T has a number of cellular plans, and it wouldn’t surprise me that some might transfer and some other plans require AT&T assistance.

See the previous link.