My workplace bought an O365 license and so I have access to O365 with my institutional email which is not hosted in Exchange (it's something different).
So I normally use this email and my password to access my O365 account online and I have there my Outlook web app, whose calendar syncs nicely with the teams calendar (I access teams with the same O365 account of course, both online and in the desktop app).
However, my Outlook web app doesn't receive any emails sent to my institutional email because my institutional email is not hosted in Exchange, and so it is not forwarded to my Outlook web app in any way. The only messages I get in this Outlook web based app are those pertaining calendar invitations. Note, this also means that I get no email for team invitations in my institutional email (since my teams is associated to my O365 account, for which my institutional email is merely a login). All this is fine with me.
What I want is to have is access to the calendar from the Outlook web app, in the Outlook desktop app, but I haven't been able to figure out how, because I don't know which account to add in the Outlook desktop app. I have been able to add my institutional email account to the Outlook desktop app, and that lets me see all my emails in Outloook. However, I don't want that, because as I said earlier this email address is not really Exchange hosted and it merely acts as a login for my O365 account.
I know it's a bit convoluted, but I haven't been able to understand the issue in any simpler way.