First of all let’s clear something. There is sharpness and there is cutting ability. A good example to understand the difference is to think an axe that can be razor sharp but doesn’t have great cutting ability (ex. cannot cut a tomato easily) and on the other hand we can have an usharpened “laser” gyuto (super thin) which has no razor sharp edge but can still have a great cut feeling.

With that said, there are various “unofficial” tests for testing both properties. Many of them consist the cutting of paper in various thicknesses and angles, other shaving human hair etc.
In my opinion, the best way to find out the performance is to use it in real situations and that means to cut eggplants, peppers, tomatoes and onions. For example, slicing a ripe tomato should be an easy task in every angle and pressure with a properly sharpened knife with great cutting ability.