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I'm not the right person to ask for that kind of differentiation... it's been a long time since I've had to do much of anything with component-level circuitry, and it's use it or lose it as they say.
My experience is mostly at the data center level. And I got real tired of having to explain to uninformed C-suite micromanagers and their sycophants why it's a Bad Idea to run the industrial AC off of the UPS, for instance. Or they're nitpicking because a UPS is 40kVA and saying 96% capacity while "only" supplying 37kW and completely ignoring the fact that we REALLY should not be running it that close to max, as stated many times, instead choosing to "investigate" why the math doesn't add up (hint: it's because the power factor was less than 1).
(And if my math doesn't add up, I'm blaming it on exhaustion and being out of practice. Roast as needed.)
You are correct, generator is the way to go, with the UPS covering for the transfer time. AC goes on the generator.
Unless you don't spec the generator to be able to handle the AC and have to do a song and dance with rolling units for every power outage. Then the AC sits idle while the undersized rolling unit just barely keeps the room below 95 degrees.
Or if you build out an office in an area famous for hurricanes and instead of a generator you buy a shitton of (physically compatible but logically incompatible) battery banks, reinforce the floor to hold the weight, then complain about not being able to have an accurate remaining runtime during an outage and bitch about people having to be sent home because it's now 90 degrees and humid inside the cube farm and why isn't the AC on battery we have so much battery.
And then the same people walk away with millions when the company gets bought out and they move on to their next victim to do it all over again.