Per that comment T135114#2476359 and the following, it is now time to change the bubble speech icon by the tray icon to remove the idea of "messages" when you click on the "notices" badge.
I've set priority as high, because CLs receive feedback about that inconstancy.
The tray icon is still on discussion for polishing: T135114: Review "tray" icon - that discussion is stalled at the moment because of vacations. When the polishing is done, the icon will be changed again.
As a reminder, the new icon: