You do not have permission to save files to this location

If you have the Paragon NTFS reader installed and it’s not working, check for updates to Paragon, and then check with Paragon support.

Or off-load the data, reformat to HFS+ or APFS, and re-load; switch the volume format to one with native support.

If you’re not swapping with Microsoft systems, I’d reformat to native.

If you are swapping with Microsoft systems and the Windows systems are on the same local network, I’d reformat and set up a file share.

If you are swapping hard disks with Windows remotely, update Paragon and check with Paragon support.

You should not need a driver from the Seagate website. macOS has native support, unless Seagate fid something unusual and non-standard.

NTSC national television system committee (or probably more commonly as never the same color) is the US analog broadcast TV scheme. NTFS is the Windows NT File System is the current Microsoft storage volume format, when not using one of the older FAT file allocation table variants.

macOS can NOT natively write to NTFS formatted volumes.

I'm betting you had 3rd party NTFS drivers installed previously that are no longer compatible with the version of macOS you're running.

As for the exFAT volume, exFAT does not support extended file permissions. Don't worry about that.

Temporarily empty the external NTFS storage device somewhere else, erase and reformat it to HFS+ Apple Extended Journaled or APFS, repopulate it, and continue on with life.

Or get Paragon or such, which can read and write NTFS.

If you’re swapping the NTFS drive around locally, consider setting up and using a file share from Windows or Mac.

Tinascousin wrote:

In Get Info for this drive, firstly I note the drive name and extension field is greyed out. Format shows as "Windows NT File System (NTFS)", which made me wonder if this was the culprit but then, as noted above, I've definitely successfully save to this location in the recent past.

If this is a NTFS-formatted volume on a directly-attached drive, there is no way you can write to it unless you have a third-party NTFS driver installed and working. Out of the box, macOS can read (but not write) NTFS volumes.

You say that you could write to it in the recent past. This suggests that you had a working driver installed – but that something has happened to your driver installation.

Incidentally, on a second external drive (Format: ExFAT") I can do everything I've mentioned above

Out of the box, macOS can read and write to FAT32 and exFAT volumes.