Any Jira Cloud REST API endpoint that returns user objects in the JSON response will return a blank email address for any non-managed users. This happens regardless of if they are set to "Public" or "Private" in the Atlassian Account privacy settings (which do not have the email address specific setting for non-managed accounts).
- Invite an unmanaged user to your instance if one does not already exist
- run /rest/api/3/user/search?query=<email address of user>
The returned user object email field is populated with the expected email address
The email address field is returned with an empty string as the value
Currently, there is no workaround.