Not to reopen this thread unnecessarily, but I’ve observed some behavior that might shed light on this issue. I believe that the Outlook app notification system is server message based, and not directly related to an actual refresh of messages by the app on the device.
Why do I say this? I recently was on a long flight where free “messaging” was available, but which prevented email and other non-message based communication apps from connecting. Throughout the flight, I received new email notifications from the Outlook app. I, however, received a no connection error when I went in and tried to refresh the actual mail app to see the messages for which I received notifications.
This could also indicate the reason why I can delete a new email notification from the lock screen, but can not delete the actual message from my inbox until I open the app (when I do have connectivity), and perform the action there.
To me, this seems like an indicator that the new message notification and inbox sync processes are completely independent.