Unread, and how to mark things read
A notification you have not read is marked, and the number on the bell counts how many there are. Opening the panel on its own clears nothing.
Tapping a notification marks that one read, and only that one. While you have unread notifications there is also mark all as read, which clears them in one go.
A message notification is also read when you open the conversation itself, or reply in it. That happens at the same moment, so the bell and the unread marker in chat cannot contradict each other.
The number updates by itself. You do not need to refresh the page.