thecodingwizard If Flarum ends up like esoTalk, there won't be anything to indicate when a user is offline.
That is, esoTalk does a couple things to let you know when a user is online: it displays a green dot next to the user's name in posts by that user, and it includes that user in the online users listing. When you can't see those things, it means the user is not online.
Since "offline" status is represented only by a lack of information, there's nothing to which you could tie any further distinctions (such as "busy" versus "away"). I'd guess you'll probably be able to leverage the "online" status for your live chat extension, so that the extension could (for example) display it's own version of the online users list. But you'd have to add your own function to display an "AFK" status for a user who is online but doesn't want to (or can't) participate in the live chat. That sounds like something that could be handled within the extension.
Just guessing, though ... good luck with the extension, it certainly sounds like something I might want to use for one of my forums down the road!