It seems that an outdated NTFS for Mac driver is rendering your external hard drive not mounting on Mac after the macOS Ventura update.
NTFS is a Windows file system that's read-only on Mac. To write to it, you must employ a third-party NTFS for Mac tool. However, a less reliable tool may cause mounting problems when it becomes incompatible with the updated system.
To resolve the issue, you need to uninstall the outdated NTFS for Mac tool and install a compatible and reliable alternative, such as iBoysoft NTFS for Mac.
This NTFS for Mac driver supports macOS High Sierra and later versions on both Intel-based and Apple Silicon Macs. With it, you can write to any NTFS drives on Mac freely without worring about not being able to mount after updating macOS.