How can I change the private relay email used in Sign In With Apple?
You can’t change their email addresses short of issuing a new app with a new developer ID. This is documented by Apple.

https://developer.apple.com/documentation/sign_in_with_apple/sign_in_with_apple_js/communicating_using_the_private_email_relay_service


Private relay email addresses have the following characteristics:

They end in @privaterelay.appleid.com.
They route emails to one of the Apple ID’s verified email addresses.
They’re the same for a user across all apps written by a single development team, and different for the same user across apps written
by different development teams.
They’re active whether or not the user is signed into a device, and whether or not your app is installed on the device. You may send and
receive email to the private email address at any time.

After the user has shared a private relay email address with your app,
they can find, view, and manage it in their account settings at
Settings &gt; Apple ID &gt; Password &amp; Security &gt; Apps Using Your Apple ID.