Не могу выйти из Apple Id.

Вы проверяли настройки / экранное время на наличие каких-либо ограничений?

Посмотрите, поможет ли что-нибудь здесь.

https://www.imyfone.com/ios-data-erase/9-tips-to-fix-there-was-an-error-connecting-to-the-apple-id-server/

https://appletoolbox.com/error-connecting-apple-id-verification-failed-how-to-fix/

https://macreports.com/verification-failed-there-was-an-error-connecting-to-the-apple-id-server-fix/

https://appuals.com/fix-verification-failed-there-was-an-error-connecting-to-apple-id-server/

https://errorcodespro.com/there-was-an-error-connecting-to-the-apple-id-server/

https://search.yahoo.com/search?ei=utf-8&fr=aaplw&p=Verification+Failed%22+There+was+an+error+connecting+to+the+Apple+ID+server

Some other things you can try. 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.