With MS Graph API you may use /beta/me/joinedGroups endpoint for getting list of groups where current user is a member. With the same endpoint you may also get isFavorite attribute for the group which shows whether or not user added group to favorites. However this endpoint has own issues: recently we found that it doesn’t return groups which were created from MS Teams: when you create new Team there also related Group is created. It is possible to get details of this group using basic groups endpoint
But if you will try to get list of user’s groups via beta endpoint such groups created from MS Teams won’t be returned:
One possible explanation could be that internally /me/joinedgroups end point is routed to Outlook services which is not integrated with Teams well enough yet: when I tried to add createdDateTime attribute to the REST url (this attribute is returned for groups from basic endpoint - see above)
it returned error saying that returned entities have Microsoft.OutlookServices.Group type:
May be this is a bug or such functionality is not implemented in beta endpoint yet. For now I asked this question in StackOverflow – hope that somebody from MS Graph product team will answer it.