iOS - Missing enrollment profile for device added after 1st setup

Hi SebastiaanSmits , thanks for your answer,

Maybe I made the wrong question, but I found some differences between devices enrolled from scratch and restored from a backup, and I though was due to something related to the enrollment profile.
And the devices enrolled later are not really supervised. Ownership is Corporate but it's all.
As example user have the possibility to remove the device and the management profile for devices manually enrolled, no matter if they're included in ABM or not, where they have not this option available for ABM devices enrolled from scratch that show the enrollment profile.
Also the behavior of the Wipe function act differently, devices manually enrolled are wiped but they're still linked to the user AppleID.
Another example, I apply a name template to all the ABM-enrolled devices, this is not applied to others.

About the backup with an existing MDM profile we're aware of that, I'll anyhow have a look on the link you posted.

JutManGraham , I had a look on the categories but looks like they're not used in our environment.
And when I created a test one it was immediately asked to pick up one on any kind of devices, not iPhones only. So it's not a suitable options at the moment.
I also tried enabling the enrollment based on user choice but if user choose to indicate a private device and ask to protect company app only it start asking to use a managed AppleID, and it's not our case.