Restore Backup from iCloud without erasing iPhone setting

Hi

I need to move all our iPhones/iPad MDM profiles in the company to a new Intune profile and remove the old MDM profile, for doing this, I am removing the old profile first and then taking a backup from all phones in include and then restore it to the factory setting, this allows me to install the new profile,

after that, I should be able to restore the taken backup via iCloud, but it's put me into a loop!

it keeps asking me to give permission to erase all content and settings and after finishing the process there is no profile on the setting and when I tried to install the profile it's asking me to give permission to erase data again!

I checked both ways, either profile installed first or backup restored first, I couldn't have both together!

I am wondering is there any way to restore the backup from iCloud without erasing the data and setting OR why I can't install the new profile on the restored phone, please?

the error comes with :

an unexpected error has occurred with phone profile installation failed the profile microsoft.profiles.MDM must be installed interactively mcinstallationerrordomain - 0xfa1