It’s almost as if the question is vague on purpose to stir up responses!

It’s almost as if nobody has actually read the question! The OP says in the first sentence that the machine is from 1998, and that they’re going to use it about an hour per day.

Still, the attraction, it got the attention for, may be the more general question.

Something I didn't see mentioned but a consideration: what's the quality of your electricity supply? I live in a location with a lot of summer thunderstorms and even with a surge protector and lighting arrestors I'm nervous about having stuff plugged in unnecessarily during storms, having seen devices destroyed by it.

That may be a factor, excellent point. Electric supply is pretty good and there hasn't been a major outage, since I was a child. Also, power lines are buried (under ground), here. (But I have surge protection, just in case, and am running all related equipment from the same protected outlet.) Which also means, I have no idea.

Power them from a pure sine wave inverter connected to a battery thats being charged. Aka a good UPS

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.

Ethernet has galvanic isolation.

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.

Doesn't an UPS have similar isolation?

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.

Most UPS that you’d plug into a socket aren’t online/double conversion though, they’re line-interactive.

Apple will always have the best RAM. They get to pick from the donut of wafer, and have testing processes rivaling that of the fabs.

I've read that electrolytic caps dry out faster if they aren't holding a charge. Temperature is a concern, but I have a surprising number of devices that worked fine before I left them unplugged for a few years and then didn't work when I powered them back up.

There's also a small amount of wear simply from the drag of electrons running through the fine filament threads of wire they are piped through. The longer this goes on the more electron tunneling will happen, degrading the CPUs performance.

We don't notice them on larger wires as the wear is infinitesimal, but in a CPU where the wire diameters are in the micron scale and below there is likely a maximum lifetime of usage before the whole system becomes inoperable.

Might be 500 years of continual usage, might be 50, I don't know and I don't think anyone has done a long-term study on how long a CPU can be continuously operated before it fails, but the risk is there.