Thank you for some clarification. "Full browser experience" sounds like a bad joke, though. Real people often have much smaller displays than the designer guys and gals. They keep forgetting about it, with their huge screens. At 1280 x 1024 the open side pane overlays 1/3 of my screen. That's not a full browser experience. That's an automatic switch to mobile view on responsive websites and unreadable content on non-responsive in a side-by-side mode.
And if the chat is not always visible, then I see no reason to have anything else in the browser window, including the sidebar that carries the messenger icon. Give me sound notification, and be done with it. I'd keep a separate tab for the messenger. Leave it on the home screen, for example. Together with the sidebar, if it's so important. But off my browser window, please. That's ridiculous.
Such a great idea ruined by execution.