If you want something expandable and built for this requirement ou of the box you should look at something like a Jackery, or EcoFlow Delta or the like. Expect to pay about 1200 for everything all included.

However you could build your own system for much less. As @ramble81@lemm.ee said you don't want to use a traditional UPS without a power inverter and that'll rob a lot of efficiency.

You would obviously scale this down but here is a pretty good how to that should give you plenty of terms and concepts to research.

https://theperfectadventure.com/diy-power-station-instructions/

Calculate your ROI first, but beyond that you don’t really want to plug a UPS into what is essentially another UPS. Quite a few units are sensitive to normalized sine waves and will constantly go on battery which negates what you're looking for.

It's fine, I have several UPSs on a critical loads panel that I'll run off an Ecoflow during extended power outages. And just for the heck of it, I've run my big office UPS directly off the EcoFlow all day. As I have rooftop solar this doesn't provide any daily benefit aside from backup, but it's perfectly fine to do so. It doesn't provide any economic benefit, most likely, though.

I would definitely use only a pure sine wave inverter. Fortunately these days it's mostly the norm.