Adding a UPS is adding another source of noise. I think the Furman, especially if it includes a voltage regulator, is exactly what you should be using for your entire system.
The reason your PC wants a UPS is to avoid lost/corrupted data during a power outage, which would happen if for instance you were editing a document, or software was in the middle of making changes on the disk. Your Trinnov and other such audio devices don’t suffer the same problems. The danger they face is the same as with the rest of your gear: Surges and long term over/under voltages.
Truth is there is no longer any TV, DVD player, surround processor or streamer which is not fundamentally a computer, with a CPU, storage and operating system. They are designed with the idea of unexpected power outages in mind, though in the event of a power outage during a firmware upgrade things could get messy.
Still, if you go down this route consider instead something like an EcoFlow or Goal Zero or Jackery LiFePO4 based generator. Many models can be used as an always on UPS but have much better $$/Watt Hour ratios than computer based UPS.

