In the New Outlook, the drag-and-drop functionality for moving sent emails to another folder or platform is not supported. This limitation is part of the design of the New Outlook, which aims to prevent accidental actions on the wrong account. In contrast, the classic Outlook allows for this functionality, which is why you may be experiencing difficulties when trying to use it in the New Outlook.
Currently, you may need to switch back to the classic Outlook for tasks that require drag-and-drop capabilities until more cross-account functionalities are implemented in the New Outlook.
References: