Well, that is actually 2000 W constant power, I would gladly prefer go another route; no carburetors, no magnetos, no oils, no spark plugs, no gasoline, no nuts&bolts, no pulling cords for never starting when needed :
'No magnetos', have we fallen through a time warp?
However, if you're used to a generator you're going to be sorely disappointed with a cheap inverter and a couple of car batteries, pretty short battery life, and I'm dubious a Temu inverter will last very long, or produce it's claimed power.
Assuming the two batteries are in series?, you're talking 83.3A for 2KW, assuming 100% efficiency - so more likely 100A or so, how long is a car battery going to last when supplying 100A?.
A nephew who is a home power nerd went through similar blind alley solutions, until he finally settled on a Tesla battery and inverter. Expensive!
I am not a fan of the Tesla company, but that doesn’t blind me to the fact that they are really quite far ahead with respect to home energy storage and power conversion.
My Tesla 6KW solar grid-tied inverter exploded probably from a mains transient a couple of years ago, perhaps not enough protection circuitry for those events. Bought another brand. So far, fine since then.
-Nothing to do with my generator that died.