Ultrasonic vibrations have been successfully used to make cutting tools more effective for a long time. It doesn't make the cutting edge sharper or amplify the force, it just moves it back and forth slightly, in microscopic imitations of a cutting motion. That does work. Though at the end of the day it won't magically make a dull knife sharp.

Ultrasonic vibrations have also been successfully used to get shit off of surfaces for a long time too. It is a common and effective method. Though it usually involves a bit more than just shaking the thing, but still...

Theoretically this knife could very well do both of those things. Probably not well enough to be worth 425 dollars, but probably entire useless either.

This test: https://www.youtube.com/shorts/PTd98UnJnnU looked fairly objective to me. It's kinda cool, but not as impressive as most demonstrations (probably shills or "official") make it out to be. It certainly didn't pass through the crust of that baguette much cleaner with the vibration on.