You can troubleshoot by referring to A 403 Status Code is Returned When You Access COS. If you use a temporary key for multipart upload, check whether you have the multipart upload permission and whether the authorized path is correct.
You can use the multipart upload API and increase the size of each part. For example, if the current part size is 1 MB, you can try to adjust it to 5 MB or other sizes, and then see how the bandwidth has been using. For more information, please see Multipart Operations.
List Multipart Uploads API needs to use a callback function. Therefore, you cannot obtain the progress directly.