Now I have a great standby generator, though, so I'm sure I'll start taking it all for granted again soon.
The power goes out a lot in the winter but at least we are cozy, particularly with today's LED/Lithium lights.
Back when I had ADSL from the central office my internet would stay up when I lost power so I had enough power to run a cordless phone and one (of two) DSL modems off a small UPS -- so I could keep 21st century comms. Once I got fiber-to-the-node most outages would affect the node so I gave up on the UPS. They're supposed to get FTTH to my house soon but I have no idea how that is going to be affected by outages.
That would depend on the source of the outage and if your power has single points of failure in common with the comms infrastructure. One would hope the exchange has generator backups to cover short complete outages, but I'm not so sure about equipment between there and your residence (does the local cabinet have a power source, perhaps a battery or its power feed being provided by the exchange and its backups, that would survive at least a short area-wide outage?).
I've certainly had full internet access when power has dropped for my (very urban) home and the rest of the local area, so at least in cases like me the exchange and infrastructure between kept running (and my laptop battery & the small UPS protecting the ONT, router, switch, and AP, kept my infrastructure going even though the desktop PC dropped as it isn't on the UPS).
After a few of these outages and typically two to three nines of utility power availability, I got a portable generator for my well (we have an automatic generator for the house, but the well is on a separate meter); but we've also had a well pump fail. That was "fun", I think the well company came out the next day to troubleshoot, and then the 3rd day to replace the pump, which took pretty much all day because of the depth of the well. At least it happened during good weather.
I've been seeing aliexpress battery + hybrid charger deals that could probably support my pump, at least for a little while, will probably do one of those eventually, especially if we build a pumphouse.