I am jumping on here because I resolved this issue in seconds, however I cannot remember the exact steps. Within Outlook, I navigated to Settings>General>Notifications and had all the desktop items turned on already. At the very top there is a link to System Settings so I clicked on that. So in System>Notifications>Outlook (new) I turned some things on - apologies as not sure what I did, I know at the bottom of these options there is Priority of notifications in notification center and I changed this from Normal to Top. Then I checked in the notification center that the Outlook icon is there. I went back to the Outlook Settings>General>Notifications and at the top saw the option to tick/check the box beside having notifications when closed (this was not there previously!!).
I hope this helps save heaps of time that I know can really spiral into a rabbit hole. Shocking this has reached 6 pages of replies and Microsoft assistance and this hasn't been solved.