I did see the cutting of badge when showing the activity bars icon on top but not left.
The finally, I found that the setting related to them in settings.json could be diff with that in UI setting in WorkBench-> Appearance, which I guess Cursor need to fix them to make them consistently.
after all, what I want is like this in vscode:
but not this currently in cursor:
NOTE: the above cursor badge shown is with the above settings.json while the UI settings like this: