Is using a power station as a UPS feasible? One of the issues I've read is that most don't have AC pass through, so it's always charging and discharging the battery.

However that seems a bit odd (with my limited electronics knowledge) as batteries don't have an 'in' and 'out' port. The AC charger input, inverter and battery are all connected to the same 12V (or whatever internal voltage it uses) rail. I imagine as long as the inverter output is less than the charger input, it won't touch the battery, as the resistance will be higher.