An EID is specifically associated with an eSIM. The iPhone 7 does NOT have an eSIM, therefore it does not have an EID.
You can not add an eSIM to a device that did not come with one from the factory.
And eSIM is part of the circuitry of the phone. a permanent part of the logic board.
A regular SIM is a physical card that can be inserted or removed.
You need to get a physical SIM from your carrier. If they are insisting on issuing an eSIM, that would indicate that they will not support the phone you have and you will need a new one.
The iPhone was discontinued 5 1/2 years ago.