I think it is going to be community servers again hosted on EA servers. Much like BF5 and 1. But in BF portal you will have a little more control over the server than you do in the current community servers
Private servers are possible you just put a password on a portal server, I’m guessing you mean no external rentable dedicated servers. The best thing to take from one of the videos posted is that we will have control over maps, game types, weapons, player counts, and be able to have admins and still be able to progress and rank up on these servers. We will have to wait and see what else becomes available or even possible after release. But I’m like if what I see and hoping that some other features are possible like creating our own game mode (but that’s doubtful).