Just in case anyone reads the parent and the takeaway is you can’t: you can still operate UniFi that way if you want to. The cloud connection and apps are optional.
Interesting. Did that change at some point in the past? I'd seen reports from folks suggesting that you were stuck either using the cloud management bits or using their app, and that a plain local web connection didn't work. Does Ubiquity equipment work entirely with a local web connection now, with no app or cloud, for all their functionality (except, obviously, cloud management functionality)?