messageTray: Expose Source icon as GObject property

messageTray: Expose Source icon as GObject property

As the notification redesign affects the API anyway, we can just
as well use the opportunity to modernize the code.

Turning the icon into a GObject property means we no longer need
a custom signal for change notifications, and the icon becomes
usable in bindings.

Since setting an `GThemedIcon` is common this also adds a convenience
property to set the icon name directly.

Part-of: <https://gitlab.gnome.org/GNOME/gnome-shell/-/merge_requests/3103>