As it seems, currently Outlook Web Add-ins do not support context menus (e.g. the menu which appears when the user right clicks on an appointment).
However, native Add-ins seem to support this (There is a "Send to Onenote" button which appears on Outlook).
This functionality is very useful, especially since Web Add-ins also do not support tasks panes to stay always open. This causes that the user needs to reopen the task pane again and again every time he opens an appointment.
Our use case would be: right click "Take Notes" which opens a Task Pane where the user can take meeting notes.
Looking forward to get the OfficeDev's feedback on this!