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You keep saying Apple-ID. But I think the account information required to ERASE a computer is NOT Apple-ID but local Admin login username.
The admin username is created when you first set up your computer, and is stored completely local to that computer. it is never even Known to your Apple-ID account.
On the old computer, the admin username and password are EXACTLY as you left them when you last used that computer. They are not connected through or updated by your Apple-ID. if you created an identical new username on the new computer, it is only identical in YOUR eyes. The new computer sees every username it has as local, and unique. it does not care if you gave it the same name as the username on another computer you own. The new computer user that may accidentally have the same name is NOT identical.
The new computer has no way of reaching back to the old computer and updating a User login password. And why would it even try -- as far as the new computer is concerned, the new user is unique in the world.
This holds true even if you created the new Username and/or password by specifying it in Migration Assistant/Setup Assistant. Migration assistant/setup assistant DO NOT modify the original computer or any files or passwords on it in any way.
So to erase the old drive, use the old Admin login, and the old password that you last entered on the old computer, and ignore the fact that you created a user with the same name but a different password on a different computer. User names and passwords are LOCAL to the computer.