Best you can do via the Graph API is fetch the userPurpose property on the mailboxSettings resource, which gives you a clue whether the mailbox is user, shared and so on. However, that's one additional call for each user, and only covers mailbox recipient types, so it's incomplete. In other words, go with Andy's suggestion above and use the Exchange tools instead.
Here's the relevant documentation on userPurpose: https://learn.microsoft.com/en-us/graph/api/resources/mailboxsettings?view=graph-rest-beta#userpurpose-values