Truncated transfer of Time Machine backup contents to new flash drive
Time Machine uses hard links to link to multiple copies of the exact same data. Hard links are one of many features that exFAT does not support.

If you were to copy multiple files that link to the same data to an exFAT drive, it would be duplicated for each hard link, potentially making the resulting copy much larger than the original.

To avoid these problems, you should probably only ever copy Time Machine backups to an HFS+ or APFS drive. If reformatting the external drive is not an option, you might consider creating a disk image of the backup directory and save it to the external drive (via Disk Utility or the command line).