"Finish changing your password" alert not going away

On MacBook Pro running macOS 10.14.6 Mojave I get this message very often with subject "Finish changing your password" and says "your password also protects access to data stored in iCloud. To finish changing your password, enter your new Password in Settings while connected to the internet."

This message was also appearing even before I upgraded to Mojave, and it started appearing the first time I changed my laptop's password. I was never able to do anything to fix this.

Details

When I click the notification balloon I see the following:

Clicking "continue" does not do anything useful except to show me another pop up with the exact same message.

I click on "details" next, and it just dismisses the new pop-up without anything happening.

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Where am I supposed to enter the new password? What Settings is the message referring to?

Thanks,

Dex