> 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).