Can you transfer your eSim to a new iPhone via iCloud?

You cannot transfer an eSIM. It is a physical part of the iPhone. The eSIM is not like a physical SIM. You cannot remove it from the phone. If you purchase a new iPhone and had an account on the eSIM, you will need to contact that carrier to change that device to a new device. They should be able to explain what you need to do.

No, nothing is stored on the sim card, so don't know why you need to transfer via icloud.

An esim is a physical part of the phone that can’t be removed. The phone number associated with it is programmed by the carrier. If you get a new phone, you need to have the carrier program the new esim with the number associated with the old one.