Another for Keycloak. Though it is probably overkill for many people’s needs in here - it certainly is for mine! But it is what I have up and running and see no need to change to a simpler option.

I think you have managed to skirt around and discount the answer to your question. UPSs are not intended to be anything but a very short term power source. They are there to provide emergency power long enough to either shut down cleanly or migrate to another long term source of power. In your example with the “home power backup”, you have that and a UPS. The UPS smooths out the power and covers the few milliseconds during the transition. Even large datacenter UPS installations operate in this fashion. Datacenters would have a secondary source of power, typically diesel generators. The UPS batteries will be sized to run the site for a few minutes - enough time to get their generators up and running and the load transferred to them.