iOS - Put Iphone in supervised mode without erasing data

Question

For work, I have to replicate the operation of a parental control application on the iOS side in order to apply certain restrictions.

Here's what I'm trying to do, put an iphone (ios15) in supervised mode without data loss and without a temporary iphone nearby.

I know this is possible because we are trying to figure out how the Our Pact app managed to do this.

For the moment my main problem is to reinject the backup made by the AC2 utility (cfgutil) without removing the supervision.

If anyone has a solution or even a line of thought, I'm a taker, thank you!