Power outages aren't common enough here that this is a big concern. And since the network is likely to be down, there is likely zero point in keeping your serve

Power outages aren't common enough here that this is a big concern. And since the network is likely to be down, there is likely zero point in keeping your server online. (Your services can survive a reboot cycle right?) If the services are required to be online, it's likely you'd want your network online as well so you'll need a battery backup for your router. So you run the Raspberry Pi on the same battery backup you have your router on.