Track verticles selection

Good day. I’m learning python for blender and stuck with pretty simple thing. I want to do some action when verticles are selected ( or at least one) in edit mode. But i cant find proper handle event for this.
For example this code:

import bpy
def depsgraph_callback(scene, depsgraph):
print(‘Vert is selected’)

def register():
bpy.app.handlers.depsgraph_update_post.append(depsgraph_callback)

register()

It should work but it doesn’t. Why it doesn’t detect changing verts selection?

Unless something changed very recently, the API does not recognize that the selection has changed mid-operation in edit mode. You have to manually update the operator (a button for the user to click after changing the selection, for example).

How then this panel works?
ammdc (1)
It does exactly what I described - reacts on changing verts selection and updates the info in the panel.
How to get the same?

Or as a solution I need a handler that tracks a mouse click. If so, which handler should i use?

why not just look at the source and find out?
image

and then you would have your answer:
image