My tests for adequate sharpness are push cutting A4 paper and shaving hair.
I used to do harder tests too but I gave up as the efforrt required was too much and the extra sharpness lasted for very little time.
Some people will slice toilet paper or cut a hair in two.
Regarding shaving there have been videos where people have shaved with an axe, after getting it really sharp (I can not see the video enki posted from here so I do not know if it is an axe shaving video)