We kind of have proxy numbers for this because we have the number of notification impressions from each source, but they also show different numbers of notifications by default. So let's also instrument the number of times people open each of them.
We already have mw.echo.logger.logInteraction( 'ui-badge-link-click', ... ) for the panel, so we'd just need to add instrumentation code (server-side, ideally) to Special:Notifications.