The unread(s) will still show in the sidebar, outside of chat and when in drawer mode. This is to prevent the confusion to show an unread count for chat on a button which is going to take the user out of chat.
This commit ensures we have correct icon and title on mobile for the chat header icon.
It also fixes a bug where the site setting was not correctly used when the user has not yet set the user option.
Both cases are now correctly tested.