Do either Microsoft Graph or Outlook REST API support importing existing emails into an Office 365 mailbox?
By definition, importing means copying emails in a way that preserves their original information, including their created / sent / received date.
I have tried these endpoints to no avail:
Thus either I have used them wrongly, or it is simply that they do not support setting date-related fields.
No, the APIs do not have any ability for importing. It's a great idea though! You should make an entry on our UserVoice forum.