Those two devices draw about 8 watts, but the UPC I bought can run for only about 10 hours on that load. It could run a lot longer except that the inverter is scaled to handle a larger load so efficiency is bad. And why the hell is it converting AC to DC, then converting to AC, then converting it to DC in some awful wall-warts.
Since you don't run the inverter for really long times, there is a pressure to put in a cheap, inefficient inverter. However, if you took out the inefficiencies, you could afford to use lithium batteries and produce a much better product for this market. Hell, maybe the thing supplies power to the phone and modem through USB-C and it is just a super-powerbank.
Basically a "micro-powerwall". Safety issues still concern me but smaller scale reduces the odds.