Thanks for the response. It turned out that the synchronize command restored the emails to their folders.
Time machine did not work, nor did the folder rebuild command.
Searching for individual emails was not the issue for me. I did not misplace or move any of the folders, all the folders were still there where I created them. The issue was that all the emails previously in the folders disappeared from all the folders in an instant. The emails were indeed misplaced, but they were misplaced on a massive scale by my computer, for an as yet unknown reason.