If this external drive is using the NTFS file system, then it appears you are using third party software to manage this external drive. You will need to update that third party software as well just like you need to update all other third party installed software.
FYI, it is best not to use any third party software to manage external drives....because you are now relying on that software to always work, but any minor OS update could possibly break that software leaving you unable to access the data on the drive until you resolve that software issue.
Usually it is best to use a file system that macOS natively supports. APFS and MacOS Extended (aka HFS+) are best if the drive will only be used with a Mac, but if a drive needs to be shared with Windows, then use exFAT (best to have Disk Utility format it). Unfortunately Apple rewrote the FAT & exFAT driver with Sonoma and some people have reported some issues at times, so your mileage may vary with it.