If you need to find out the “domain/public/private” network connection profile on each machine, you need to set a custom hardware inventory class from SCCM.
This class is called MSFT_NetConnectionProfile under root\StandardCimv2
The result you get is like this:
To make this custom hardware inventory class available inside SCCM, you can follow these steps:
Once this class has been added, you can enable it in future hardware inventory.