They say private networks ... they do not say who owns or manages the private networks ... For all private networks could mean is a enterprise grade private network... I would be seriously skeptical about this ... The last part on the link about LWA is pause for thought. This does not look like it is meant for end users.
Getting SIM cards for a private 5G network seems like a pain. eSIM would avoid the need for physical cards on paper, but I wonder if iOS and Android will take eSIMs from a random entity without the cooperation of Apple and Google respectively.
I remember hearing that some conference at some point did its own 4G network with its own SIM cards. They had gotten permission to use licensed spectrum for the duration of the event. Unfortunately, I do not remember which conference. If I did, I would look at what they said about how they got the SIM cards for it.
eSIMs all need to have a chain of trust all the way back to some GSMA gatekeepers. As usual with all kinds of mobile telco stuff, it's never open and really doesn't like people messing around (partly because people messing around might find how much of a broken, insecure and "designed by committee" shit-show most of it is).
You have to buy your own base station. Its for IoT, factory automation, home use. 5G small cell architecture.