Update Apple ID Settings goes into a loop

My daughter has been having this problem for weeks now. Basically, the settings app has a notification to update Apple ID Settings because other services can't work until we do. Example of the services that she can't access as a result is turning on iCloud Keychain, and entering the Account Recovery and Legacy contacts. When you look at the notification and click "continue", it asks for the Apple ID password, which we enter, then it asks for the Phone's passcode (sometimes it may ask for the passcode of other/previous devices using her Apple ID), which we enter correctly. However, after a minute or so, it simply goes back to the same screen asking to click continue to update apple ID settings. So it goes into a loop and it never clears. It also does not complain that the password or the passcodes we enter are wrong. We have tried every trick posted online, including logging in and out, restarting the phone, restoring the phone with itunes and even buying a brand new phone (one Apple

agent suggested it was a hardware issue). However, none of that helped. We logged her in to an old iphone 7, and the update apple ID setting does clear, but the IOS version on it is 15. So it appears to be an issue with IOS 16 and higher, which what she has on her iphone 14.

I spent numerous hours with Apple support and opened multiple support tickets and even sent them the phone diagnostics. They eventually called back a week later saying their tech team believes it is a software issue and that I should update the software as soon as an update is available. An update was pushed yesterday and we

updated, but the same problem is persisting. We also found many people posting online about this very same problem for months with many software updates since they posted their issue, but so far nothing is fixed.

Our whole family is running the same latest IOS and we all have no problem except for my daughter. So although it looks to be an IOS issue, it is unclear why it happens to some people but not others. It is frustrating that Apple is not at least giving people some guidance on how to deal with this rather annoying problem. It is not really about the annoying notification that won't go away. More importantly is the many critical security services in the background that won't work until this problem is resolved.

If anyone knows the trick to fixing this or some insight into what exactly may be causing this problem, I would appreciate the tip.