We currently provide extra status info in Unity (on the app icon) but we haven't done any work for other WM's, we'll keep this open for that request.
Steam doesn't run the icon UI, so left/right click is not Steam's choice.
I agree with this
@gdrewb-valve, sorry to bump this issue, but concerning left/right click, I just want to point out that plasma (KDE) sends a dbus signal on "left" click:
method call time=1480168156.675115 sender=:1.30 -> destination=:1.166 serial=10481 path=/org/ayatana/NotificationItem/steam; interface=org.kde.StatusNotifierItem; member=Activate
int32 2711
int32 1021
And, of course, on "right" click:
method call time=1480168158.016969 sender=:1.30 -> destination=:1.166 serial=10482 path=/org/ayatana/NotificationItem/steam/Menu; interface=com.canonical.dbusmenu; member=AboutToShow
int32 0
method return time=1480168158.062980 sender=:1.166 -> destination=:1.30 serial=23 reply_serial=10482
boolean false
So, restore on left click (or, a bit worse but easier, context menu) should be pretty straightforward to implement 😃
As mentioned above Steam does not run the icon UI, that's a piece of non-Valve software called libappindicator.
Nothing extracted yet.
In Windows, the system tray icon changes to reflect when Steam is downloading or in offline mode, and its tooltip shows things like download speed and progress. So far the Linux version, at least in KDE, does not. I don't know how the system tray behaves in Unity, Gnome Shell, and so on, but KDE's offers a pretty complex feature set. For example, here's what Amarok looks like when it's playing a song and you mouse over the icon:
As you can see, there's plenty of room for additional information; note also the modified icon with a play symbol on it.
In addition, Steam's systray menu is currently only accessible by right clicking, whereas in Windows, left clicking works also. I've gotten used to left clicking, and most of my other system tray icons do something when you left click on them -- in some cases (such as the clipboard), only left clicking does something. Something to think about.