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AC UPS expose the complicated issue of reactive power or power factor. 12000VA means 1.2kW at a power factor of 1, or unity. Connect a computer, and it’s more complicated…
Incandescent bulbs are resistors - resistive loads, at a unity power factor = 1. Simple.
Most computers are reactive loads - both inductors, and capacitors, so actually place more demands on a UPS, which electrical engineers cope with via a non-unity power factor.
Without two days in Wikipedia, or a course on imaginary numbers, plus AC phasors, it’s complicated.
De-reate the UPS by (say) x0.8 for inefficiency (heat losses), de-rate for power factor by (say) x0.8 (as the PSU is capacitive and stresses the UPS more), then measure that the computer manufacturer’s data is worst case, so the steady state current draw is really only a fraction of that on the back of the PSU so it might still work!
I’ve seen a computer draw 1/10 of the data plate when running happily, with more for startup - just not the full whack. Testing is needed as inrush current can blow fuses (e.g. lots of amps are needed to start spinning NAS mechanical disk platters; SSD less so).
Data centres turn on kit in stages to avoid inrush currents when racks are first turned as once on the load reduces a lot. If you have several larger computers, several relays can do the same to allow start up to be staggered.
Safety
Looking at the diagram, the risk is several independent switches that rely on Wi-Fi, and could connect two mains sources to the UPS, and two chargers to the 12V battery.
Some UPS have multiple inputs, but here, it would be much better to use a break-before-make arrangement guaranteed in hardware to make it impossible for a microwave oven to spam 2.4GHz and cause a serious loss of magic smoke. APC used to offer 1U boxes for this, but a change over relay might be enough as you have a UPS to smooth out the AC going to the IT kit.
Efficiency
As mentioned in passing above, conversion of AC to DC or the other way is not perfect. An inverter or AD to DC charger may only be 80% efficient, loosing a chunk to heat.
You’ve effectively drawn two UPS in series, as a UPS is just a charger + battery + inverter in a box.
Going from solar DC to AC (inverter), then DC (inside the UPS), then to AC (although some UPS bypass the AC->DC->AC automatically unless in test), then down to DC (in the computer) will loose energy at each stage.
The hard bit is solar battery designers aren’t used to IT kit, and UPS designers only expect one power source.
I’d run the router (assuming 12V consumer CPE, not a Cisco 6U box) directly from the 12V battery. I use a cheap CCTV 12V SLA battery-backed supply as a UPS for mine.
12V replacement for ATX power supplies exist, but realistically unless you are building a remote mast site, a cheap UPS or separate inverter will be cheaper.
Accepting the losses of a cheap UPS to smooth out breaks in power might be OK, but I’d suggest you’re being too ambitious in trying to connect everything to every power source.
(I did wonder about schotky diodes to attempt to charge the UPS batteries directly from solar, but my guess is the UPS will freak out with higher than expected charging voltages on the battery monitoring terminals. Not worth the risk.)
this post!