The user does not receive the confirmation email

When a user requests an email address change, they do not receive the confirmation email. (Test emails in the general settings are delivered successfully.)

Mail server issue, mail probably goes to spam because it has link

Yes, it was that simple. I hadn't noticed it. It's the phone's fault for not having a spam folder.

I was mistaken; the emails aren't in the spam folder either. When I click on "change email," it redirects me to the home page.

No it's usually low email domain authority.
You create mail and start sending emails with link - that usually looks like spam.

In user-profile.php, I was using code from an older BETA version. I updated the code snippet to BETA version 1.8.1, and confirmation messages are now being sent correctly. However, a minor issue remains: after I confirm the change, the email address displayed under "Current email" does not update immediately—it continues to show the old email—even though the new email appears in the "My Profile" column on the left. The update only takes place after I close the site completely and reopen it using the new email.