Updating Apple ID settings stuck

Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Backup - Restore your device from an iCloud or iTunes backup.      

A possible quick fix is signing out and back in to iCloud.com then restarting your device.

But, see Update Apple ID Settings stuck https://discussions.apple.com/thread/7934284. Some have been able to fix the problem one way or another.

And see Getting a message to Update Apple ID Settings on iPhone, iPad, or Mac?

https://appletoolbox.com/update-apple-id-settings-on-iphone-ipad-or-mac-after-changing-your-password/Try some of the procedures given even though getting stuck is not covered.

According to a post in this discussion, this is a 'new' known issue that Apple is working on.  

https://discussions.apple.com/thread/251180098

Settings - Update Apple ID Settings When It Won’t Go Away.    

Settings - Update Apple ID Settings When It Won’t Go Away (2).    

You can only use an Apple ID in 10 devices/computers. You are limited to 5 computers.