I slipped a decimal place in the capacitance I think and changed the value above. That’s a huge capacitor (or several).
I don’t think most supercapacitors are used directly but have a switching converter so more energy can be extracted by allowing more voltage drop at the cap.
I have a lightly loaded UPS for my routers and such so am thinking of injecting power from UPS on unused ethernet lines. The failure of the main power line could be detected and shutdown the Pi. From what I have read NUT is a UPS supervisor that can run on the Pi and handle everything including restart.
Looks like it could even handle multiple machines via network communication.