Unfortunately this is not possible. The reason for this is the use case of the General tab and Update Status are mildly different. The General tab will provide you an area to "Edit" the details about the project, where Update Status is an "Update" speaking on behalf of the progress of the project. Therefore to interact with the New Status field you'll need to click on the green "Update Status" button.
Any further ways I can help you with this, please let me know!