Typically you'd have a server running on a device on each UPS, and the clients would be the other devices also plugged into that UPS, so when that UPS is low, everything plugged into it will turn off. If you have another UPS elsewhere in the house, you would have another server installed on a device there so it can monitor that UPS that it is plugged into, and tell the other devices also plugged into that other UPS to shut down. Without knowing the layout you are running though, there's no way to know if NUT is what you need or want.

So in your case it would likely be to plug your server and nas both into the same UPS, and when the server detects the UPS is low battery, it will tell the NAS to shut down. This would also require the switches/router/whatever to also be on a UPS to hold power of course. So then it basically becomes each little cluster of devices that need UPS would also have a switch nearby that is also on the UPS