Can't unassociate old Apple ID email from iMessage

After I updated my iPhone 7 to 14.7 and 14.7.1, my phone asked me to sign into my Apple ID account, except using an old email address that I no longer use for my Apple ID. I replaced it with my current one years ago. Expectedly, when I enter a password for that, it replies that the account is no longer valid. It does this every time I restart the phone.

I've attempted to unassociate the old email address from my iMesssage. I was able to remove it from the "YOU CAN RECEIVE IMESSAGES TO AND REPLY FROM" list for both iMessage and Facetime. But I want to re-add my current Apple ID email address to that list. So I tapped "Use your Apple ID for iMessage". It responds with "Use the Apple ID "<my current Apple ID email address>" for iMessage?" and presents buttons "Sign In", "Use Other Apple ID" and "Cancel"

When I tap "Sign in", nothing apparent happens.

When I tap "Use other Apple ID", it responds with the "Apple ID Sign in Requested" pane. I enter the credentials for my current Apple ID and a spinner appears in the upper right corner for many minutes and eventually responds with this:

iMessage Activation

Unable to contact the iMessage server. Try again.

Which is strange because when I enter an incorrect password, it immediately responds with "Verification Failed"

I've also reinstalled the OS and restored from iCloud backup, but the problem resurfaced.

Is there some hidden corner where my old Apple ID email address lurks and I can remove it? Is there a solution for this that doesn't involve wiping my phone entirely and not restoring from backup?