"The operation can't be completed because you don't have the necessary permissions" usually pops up when you're unable to delete or save files to an external storage device on Mac.
What file system is your external hard drive formatted with?
You mentioned that there's no "Ignore ownership on this volume" on your drive, so it's not likely formatted with APFS or Mac OS Extended. Besides, your drive apparently supports permissions, which rules out exFAT and FAT32. Therefore, It appears to me that your drive is formatted with the Windows file system: NTFS.
If you're not clear which file system your drive has, you can open Disk Utility, and select the partition of your drive to check it. The information is displayed under the drive name.
If it is NTFS, you need an NTFS for Mac driver to work with the external disk. By default, macOS can only read NTFS-formatted drives but can't write to it. To delete or save files to the drive requires the write access that only third-party software like iBoysoft NTFS for Mac can provide.
You can install it for free from the button below.
What it does is that it provides read and write access to NTFS drives on Mac, enabling you to open, view, modify, delete, and save files on it and copy files from your Mac to it. Another highlight of this tool is its automount ability, which saves you the trouble of relaunching the tool after restarting your Mac or reconnecting the NTFS drive.
If it's not NTFS, consider backing up data on the drive and reformat it. You can format it with APFS or Mac OS Extended if you only plan to use it on Mac. If you want to use it on both Windows and macOS, choose exFAT or FAT32.