I mean, there are 12V native battery systems out there, stuff like vehicle stuff.

Assuming that the 12V power supply on the router is permissive enough to take a certain amount of variation, I imagine that you can probably just put a 12V deep-cycle battery on the thing on the thing and directly hook up a 12V charge controller in parallel.

I dunno whether there’s some sort of voltmeter that you can connect NUT up to.

Personally, my position is that if NextCloud or whatever can’t handle power loss without corrupting data, that’s a bug with NextCloud. I mean, sure, it might not be able to complete an operation if there’s power loss while it’s running, but that shouldn’t result in corrupt data.