Do you have any examples? I haven't seen what you're describing despite shopping UPSes, but something less than $100 that could last 10+ hours would be amazing.
My $200 1500VA/1000W CyperPower UPS could handle a short one or two hour storm, but storms can last for 10+ hours here during the wet season. One long power outage could cost me a lot more than $1000 in basement damages (my basement is finished).
But a lead acid battery might last 5 years where the pila battery is designed for 10+ years, so you're looking at $400 total on batteries. That quickly gets close to the $1000 for one pila battery.
I want to believe $100 is all you need, but to me the math with the numbers that I've seen suggests $1000 is not unreasonable for something like this.
You buy lithium battery (lifepo4) not agm, much longer life time. I have exactly the same Vevor inverter + lithium battery total cost was 400$. But I regret doing this setup, I should have just gotten Ecoflow power station, it's a bit more expensive but more versatile.. You can take it with you anywhere