>Is an activated eSIM linked to the device's MAC address, making it impossible to use with a different device?
After an esim is "activated" it's bound to the esim chip. By design, you can't copy it onto another esim chip or device. If you want to transfer devices, you need to ask your carrier to issue you another esim.
That should work, as "physical eSIMs" are usually not bound to the device they're in in any way. Your provider might restrict the set of allowable IMEIs conencting per SIM (profile), though.
If that is the case, what would happen if we transferred the MAC address along with the eSIM? (assuming you have a jailbroken/rooted phone)