UniFi Network Appliance can indeed migrate over to UniFi OS Server. Also, as of now there are multiple options for running OS Server. What is being mentioned is referring specifically to the app (addon) for Home Assistant; it seems it will no longer be supported and no migration path planned.
You can run a dedicated system for it, or a virtual machine. You can also get it working in an LXC container, and I’ve even heard of someone somehow getting it to all run inside docker (not sure how they pulled that off).
I would obviously suggest you download a backup from your Network Appliance and look into setting up a VM or LXC and try installing OS Server. Once running, you can restore your backup and you should be good to go.
As an aside - once your AP’s are configured, you don’t need Network running 24/7. You’d only need it to check settings or modify them - your wifi will work just fine w/out Network running for a while.
Further clarification - only the UniFi Network Application app, not the UniFi integration.