not dealt with such a thing, but a decomissioned phone or laptop is the most obvious solution. they come with batteries, have seamless transition between power and battery, and you’re reusing shit nobody wants no more.
laptops you can get cheap when they have like busted screens and any reasonably modern (like decade old) can operate in sub-5W territory; coupled with a good battery, that should provide you with tens of hours of battery powered use, and you can expand that, with powerbanks and such.
alternatively, a cheap phone that can run postmarketOS or mobian. even lower consumption and more options to extend power availability.





I am the first to pile on shit on people who are like buy new stuff, but in this instance, yeah, get a $20 laptop with a busted screen or sumsuch, install debian, and use it normally (docker compose).
you need the least amount of movable parts in this setup and yours is just too off kilter for a server.