Using outlook.com calendar with Gnome Shell (Gnome 3) was an almost impossible task for Linux users and that's due to EAS (Exchange Active Sync) protocol used to communicate with Microsoft.
Now, using EWS (Exchange Web Services), integrating outlook.com calendar (mail and contacts also) into Gnome Shell it's just a simple task, available for Linux Desktop users.
The whole process is handled by Evolution (and the evolution-ews extension), configured using GOA (Gnome Online Accounts) and an App Password generated within the Microsoft account.
First we will need an Microsoft App Password, available here: https://account.live.com/proofs/AppPassword; This link should send you to the right place where an App password is generated, if not, from https://account.microsoft.com/ go to Security (top menu), more security options (bottom of the page), Create a new app password (middle of the page).Second, we need to install evolution (a Linux alternative for MS Outlook) and the evolution-ews extension.
sudo apt install evolution evolution-ews
Third, open Online Accounts Gnome App (tip: you can press the Win Key from keyboard and type something to search for, ex: online), select 'Add an account'-> Microsoft Exchange (not just simply Microsoft).
Here, enter your outlook.com email address, the Microsoft App password, expand the 'Custom' area and again, enter your email address (same as above) as Username and, important, outlook.office365.com as Server. Be sure that your setting looks like the picture below, then hit Connect.
|Gnome Online accounts, Microsoft Exchange outlook.com EWS|
That's it, you are now connected to outlook.com, your calendar events can be managed within the Gnome Calendar App, your appoitments, birthdays and tasks would be displayed in the Gnome Notification bar.
Same for the contacts (available in the Contacts App) and emails (all of this also available in the Evolution App). If you don't needs or use outlook.com for email and contacts (that's my case, i'm only use calendar from outlook.com), then, using Online Accounts App, for the new Microsoft Exchange account created, you can toggle on/off Mail/Contacts/Calendar, just keep what exactly need.
If you need to fine-tune some calendar functionality (ex: change calendar colors, disable the local one, set outlook.com as default calendar, etc) just use Evolution for that.
Some tests for the calendar sync interval: sending events, real-time; receiving events, ~10 minutes