Move menu button to date picker element and add notification badge on it

[h5vx]

• The "menu" button is button that opens the sidebar
• Currently it is placed in header on top of page and can be scrolled away from screen
• Currently there is no way to see whether there is a chat having new messages

1. It should always be on screen when sidebar is hidden
   • To achieve that, we can move it to sticky date-picker element
   • Maybe, we should leave it on sidebar, but place it on date-picker when sidebar is scrolled away
2. The red circle notification badge should be added to menu button if any chat in chatlist receives new message
   • This badge should be removed from menu button when user opens the sidebar