What's actually going on
Your disposal is leaking from the top rim, where it bolts to the sink drain. That's the flange, and the seal there has failed.
The power outage is mostly a red herring. Either you crawled under the sink after the outage and noticed something that was already there, or the hard restart jolted a tired seal loose.
Here's the mechanics of it. When power returns, the disposal restarts with a sharp mechanical shock. That vibration travels straight to the mount, and if the plumber's putty under the flange has dried out (which it does over 5 to 10 years), that last shock cracks the seal.
The good news: this is one of the more DIY-friendly disposal repairs. Most people fix it for under $20 in parts and an hour of work.
The usual suspects, ranked
Nearly every after-outage flange leak comes down to one of two things: dried putty or a loosened mount. Start there before you buy anything.
Dried plumber's putty is the top cause. The putty that seals the flange to the sink drain hole shrinks and hardens with age. Once it cracks, dishwater and sink water seep between the flange and the metal, then drip down the disposal body.
A loosened mounting ring is a close second. The disposal hangs from three screws on a mounting bracket. Years of running vibration slowly back those screws off, and a hard restart can drop the whole assembly a hair, breaking the seal.
Less common but worth checking: a worn fiber gasket between the flange and mount, or flange bolts that corroded and loosened unevenly. Both let one side of the seal open up.
The rare one is a cracked housing that only looks like a flange leak because water runs down from up top. If your kitchen froze during a winter outage, check for this before you waste time on putty.