Profile installation failed, and stuck during a new phone configuration

See this --> If you see an error when you update or restore your iPhone ...

Profile options will exist, only if any profile installed by your corporate / organisation / enterprise / School Management then please contact the system administrator of your corporate / organisation / enterprise / School Management

If you have installed any profile on your own --> Install or remove configuration profiles on iPhone - Apple ...

I have 4 devices none of them have any MDM or profile on my devices

I am unable to comprehend the actual issue you are facing.

There are two restores.

1. Restore to factory settings:- Restore your iPhone, iPad, or iPod to factory settings - Apple ...
2. Restore from a backup:- Restore your iPhone, iPad, or iPod touch from a backup ...