Remove the back and forward buttons
The existing back and forward buttons don't seem to provide a lot of value. I suggest they be removed.
They can actually remove state from the client app! For example, clicking the back button a bunch of times will remove recently added contacts from the Chat pane.
Adding hotkey popups when you press Ctrl or Alt would expose that you can in fact quickly move from pane to pane, without having to click Back/Forward a bunch of times.
Another option might be enabling Ctrl-Tab to switch between the last two active panes.