[Desktop App] For notifications in other instances, give notif bubble on the profile picture

Seeing an alternate instance notification is only really visible via the push notification / desktop notification. There is a lack of visual indicator for this when the app is at rest (not clicked into the account switcher where the current notification bubble is).

It would be cool to see a notification bubble that displays the cumulative number of all notifications across logged-in instances on the corner of the user's profile picture on the bottom left (similarly to how a server shows notification count), as that is used to access the switcher to discover which instance gave the ping.