They promote their cloud controller pretty strongly, followed by the Cloud Key, which is their own preinstalled self hosting setup, but the self-hosted UniFi Network server has stuck around. (It changed names a couple of times; it was the "UniFi Controller", then "UniFi Network Application", and now "UniFi Network Server".)
Terrible little underpowered device that frequently wouldn't come back up after losing power.
I switched to Aruba because of the cloud key and haven't looked back.
Right now it looks like UniFi OS server doesn't do anything the prior self hosted stack does already. Presumably though they are planning to roll out some of the other parts that currently aren't in the fully self hosted stack.
It never went cloud-only. You could always self-host.
They've had different versions of cloud hosted offerings over the years. A few companies have also offered their own cloud hosted instances.
There's also been a container version for quite a while too.
Gen 1 cloud key: https://dl.ubnt.com/qsg/UC-CK/UC-CK_EN.html
Gen 2 cloud key https://store.ui.com/us/en/products/uck-g2
Container from linuxserver.io https://github.com/linuxserver/docker-unifi-network-applicat...
In order to configure, check what was going on I needed to run app on my Windows computer. I was looking into using docker or something like that, but I switched to another vendor.