How can I power my sump pump in a power outage?
In most cases an extra sump pit is pure plumber profit - if the sump is not tiny, the backup pump can use the same sump, and just be set to come on at a higher water level.

The practical problem with your vision of "a battery with a 110V outlet" (battery charger, battery, and inverter) is that is entirely possible, but wickedly expensive; also, batteries don't last forever, both in the "length of power outage" and the "number of years before you have to scrap them because they no longer work at all" sense, so it gets even more expensive. Sump pumps with a battery backup built in are made - they have many of the same problems, but usually skip the added inefficiency of converting back to 120 VAC and just use a DC pump.

If you have utility water, and such things are acceptable to your utility, the water-powered sump pump has the benefit of being fairly inexpensive to own, being based on a power source you don't have to buy and maintain. You will get a big water bill if you need to use it. If you have a well pump, it's useless.

Anything depending on you running a generator depends on you being home, the generator being functional, and adequate fuel for the generator being available in the event of a prolonged outage - which it often is not, since the filling station does not have power either. You can expensively address most of those with an auto-start natural gas powered unit if you have natural gas available...

You can also use only tile or concrete for surfaces in your basement and not put things that would be bothered by getting wet in it, so that the occasional flood is less traumatic. How badly or quickly it floods if you turn the sump pump off might guide your thinking on this. It can be very expensive to build and maintain a pumping system that will work though a long, widespread power outage.