I'm not sure it is what you mean, but gnome-shell should display notifications for unread emails and for calendar alarms when a google account is configured in gnome-online-accounts.

Apps display notifications. If you have online accounts set up in your Calendar or Mail app then those should be displayed by the respective apps. This bug is about enabling, for example, a GMail app (an Empathy web app perhaps) to use the OS notification system.

Well, the problem is that some application developers refuse to handle the notification of new emails in the background (bug #651347), and since gnome-shell designers want to remove the minimization of windows, users are stuck...

(In reply to comment #3)
> Well, the problem is that some application developers refuse to handle the
> notification of new emails in the background (bug #651347), and since
> gnome-shell designers want to remove the minimization of windows, users are
> stuck...
That report doesn't quite deal with the same problem: you're asking for evolution-data-server, to show mail notifications instead of Evolution.

So this is completely orthogonal to what Jon wanted to tackle with this bug, which is about *Web* apps interaction with the Shell. ;-)

Yes Milan, my answer was only a response to the part where William said that "Apps display notifications". For the rest, it's off-topic in the context of this bug report.

Jon, do you think this could be closed as a duplicate of https://bugzilla.gnome.org/show_bug.cgi?id=653646 ?

Yeah sounds right. I'm not entirely sure what I mean here.

*** This bug has been marked as a duplicate of bug 653646 ***