Forward guest notifications to the client
Spice nowadays is capable of forward guest notifications to the client. See https://gitlab.freedesktop.org/spice/spice-protocol/issues/2
As of comment https://gitlab.freedesktop.org/spice/spice-protocol/issues/2#note_10443, SpiceMainChannel in spice-gtk emits "guest-notification" signal with the details of the notification. We'd just need to throw App.send_notifications () (see https://gitlab.gnome.org/GNOME/gnome-boxes/blob/master/src/app.vala#L455)
UI/UX
We would have to discuss how to expose this preference to the end user.
My suggestion is to use in-app notifications, asking the user to authorize the notifications to be forward. Something in the lines of browsers' Push Notifications https://blog.chromium.org/2015/04/reaching-and-re-engaging-users-on.html