That's not good enough - everything attached to the computer (including network gear, unless it's fiber) must be powered by the same UPS, or you have pathways for lightning current to enter.
Some UPS for consumers even have an ethernet through-port so you can connect your internet cable from the wall to the UPS before it touches your router.
That's functional isolation. Yeah, they're individually tested to 1500 Vrms (or so the factory in china claims), but that insulation is still just the very thin lacquer of the windings and maybe lacquer on the core. There are more expensive (and physically much larger) Ethernet transformers for medical devices and such, these have actual double/reinforced insulation and are tested to much higher voltages.
Typically the Ethernet shield is also only alibi-insulated from the device's ground. Sometimes not at all. (Personally it's always funny to me to see the fat 1kV/1nF capacitor from the shield to the device ground and then the metal of the socket is just bunched up with basically no clearance against the metal case or something like that). This can of course be avoided by simply using unshielded cable.
A online UPS has in line: a rectifier with its transformer and output-smoothing capacitors, a huuuge battery, surge capacitors, power transistors, another transformer and more capacitors. And only then comes the actual device with its PSU.
It takes an awful lot of power to smash through these multiple layers of insulation and bypass all the capacitors, at least if the PSU is properly designed (specifically, clearance between the various power / ground domains).
In contrast, Ethernet transformers are tiny small little things.
Yes, but only the transformers will provide the galvanic isolation. And if the windings are not physically separated then you are basically in the same situation.