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.