I thought for sure I had it solved. I checked the SSD with Samsung Magician, which is supposed to read the condition of wear on it, but it got a perfect score.
I thought it needed to be reformatted from NTFS to exFAT, which I did, and recopied all the data from backup to it, which took a day.
I plugged it into my TV, fully confident that I had solved the problem, but the same folders still show as empty, both on VLC and with a file manager app for Google TV (Android).
It's a deeper mystery because the files are fully accessible on a PC, and even on my S24 smartphone, but not on the Sony TV, even after all the latest updates.