YouTube collapsed the “replies to my comments” and “activity on my comments” notification options into a signle one. This extension filters out the latter so that you only get notified about the former.
It does this on the network level by intercepting the notifications YouTube’s API sends to your browser as you open the notification dropdown. That’s what it needs permissions for.
Unfortunately, I can’t see a way to modify the number that gets displayed on the notification bell icon in the same way.