OK, thanks for that. The owners thing you can ignore. exFAT doesn't have the concept of owners of files, so that's not terribly helpful or important.
As for the "missing" stuff, were you expecting files to be there? I ask because you didn't actually say if you expected stuff to be there and it's missing, or you were just surprised that space was taken and no files listed.
If you thought it was empty and just want it back in service, use Disk Utility to format it again. DU can format exFAT just fine.
If you thought you had files and they are not there, you can try the First Aid process in DU to see if there is anything wrong with the structure of the drive. That should not harm the drive if the data is at all recoverable, but be aware that it COULD cause you to lose files if it determines that it thinks they are not recoverable.
A third alternative is to try to read the drive in a windows PC to see if it can see the files (if they are there) on the drive. It's possible that if you last wrote to the drive on a Windows system that it could be read on a Windows system. That's a long shot, IMHO, but probably worth trying.
And of course, there is the tried-and-true, eject and reinsert approach to see if it's just a glitch, but I suspect you have done that already, probably multiple times, right?