The unit is set to come on automatically when regular power is cut.

Such an option is not available, but it is a clever idea.
However, it would require rewiring of every home, and separate meters for the optional vs. priority. Then, power to the optional could be shut down to focus on priority.

When the power is out, the generator will support a part of the house.
Thr refridgerator, the freezer, the microwave and oven, the satellite dish, and the living room tv, and the modem.

The generator is a costly, and frequently dangerous option.

As @Patty_Melt said – houses are not wired that way. There is only one input for a house, and power gets distributed within the house.

Another underlying problem – who decides what is essential? If a person has a ventilator or a breathing machine, how could the system know to allow IT to run, but not the TV. They are both plugged in to outlets.

As has been mentioned, a generator can be hooked up to do that and the owner can decide what are their priorities to keep running. But not every household has a generator.

Probably my small (7’ x 14’ x 5’) heated indoor swimming pool.

It would be possible to use home automation to do this without rewiring the entire house. Of course, we all know that people would not respect their neighbors. Tragedy of the Commons in action.

I have 2 generators. a small 1100 W portable, and a larger 4400 watt 220 Volt that can run my house.
My basement sump pump is number #1. I have an outlet on my porch that is connected to the sump pump breaker as well as the basement lights in the area. If everything goes bad I can backfeed, illegally, the small generator and keep the sump pump powered.
Next is the refrigerator and the freezer. I can backfeed them as well if needed.
After those items nothing else is very important. Everything else can wait until I fire up the big generator or the power comes back on.