The reason why you can't copy files from your Mac to the NTFS drive is that NTFS is a proprietary file system owned by Microsoft and has only read access on Mac. This is a driver issue but not a permission issue.
To copy files to the NTFS drive on Mac, you need a third-party program like iBoysoft NTFS for Mac. It will allow you to read and write to the NTFS drive on Mac like it's formatted natively for macOS. With it, you can copy, move, edit, delete, and save files on the NTFS drives freely.
This driver will automount NTFS drives on Mac, saving you the time for relaunching the software after a reboot or reconnecting the drive. Besides, it's compatible with Intel-based, T2, M1, and M2 Macs running macOS High Sierra and later.
Apart from mounting NTFS drives on Mac with read/write access, it also enables you to repair NTFS drives on Mac and format other drives to NTFS.