Description of the need
When a user changes their email address, Backdrop should send an email with a unique link to the user with the new email address so that the user is required to confirm the change.
This is the patch that would be the closest to what will work here: https://www.drupal.org/project/drupal/issues/85494#comment-450598.
In reading the drupal.org comments, this change should not allow someone to change both the password and the email address at the same time. And there should ideally be a way to keep sending notifications to the original email address until the change is confirmed.