I'm trying to find how I can use the microsoft graph api filters to get the entries in a calendar, but only those that have a category specified. Is this possible?
As of now this is not possible, there is a way to filter categories in a simple way like below which has 'Red category' in an event in a calendar and you can get it.
https://graph.microsoft.com/v1.0/me/calendar/events?$filter=categories/any(x:x eq 'Red category')
As a work around you need to pull all the events and then check for empty array in all events by writing the code on your end and get the required ones.
You can also create a feature request for this kind of scenario by going to Microsoft Graph Feedback Forum so that in future the Microsoft Graph Product team may implement it.