External hard drive not mounting after Ventura update

Remove Paragon NTFS software as you must have had it previously or you wouldn't have been able to write to the NTFS disks. It likely broke when you upgraded Ventura. You have the option of upgrading Paragon NTFS but it's licensed software. So if you don't need it just remove it entirely.

FORMATTING WILL DESTROY ALL DATA It's easy to reformat a drive on macOS. Open Disk Utility, click View -> Show all Devices. Identify the correct drive you wish to format. Highlight the top most tree-branch listing the hardware name of the disk. Click the Erase button and choose a filesystem.

The APFS filesystem is designed for SSD primarily, while it does work with HDD it will experience fragmentation that isn't possible on SSD. Formatting an HDD to APFS is mostly fine for say Time Machine due to the way APFS snapshots work. I would recommend that you choose HFS+ for an HDD that just holds data.

Copy the data from the NTFS drive over to this newly formatted drive using Finder and drag and drop.

Tip: ⇧ + ⌘ + Period key will toggle hidden files ON/OFF

If you need cross-platform compatibility with Linux, BSD, Windows, macOS, etc. then the filesystem format you want to use is ExFAT.