There is a saying that z is the last of the 26 English letters, and sleeping means the end of the day, so the last letter "z" is used to mean the last thing in the day "sleeping".
Another way of saying it is that people will curl up when they are asleep, which is very similar to the shape of Z, so Z is used to indicate sleeping.
The legend of the origin of "zzz"
It is said that an American cartoonist wants to describe a person's snoring, but he doesn't know what to do. Do you write sleep on the screen?
At this time, I found that people snore when they are asleep, much like the sound of sawing wood. Later, cartoonists began to use "zzz" to mean sleeping and snoring.