So I deleted it. I should have stopped right away because it was deleting everything in the root directory!
After seeing the glitched folder I first went and updated my WinSCP installation before trying to delete it.
Some more details:
Created a file named "20220830_setlist.html" from the right click menu. It came into existence with the folder icon, and it causes HTTP 404 errors from the browser. Inside of WinSCP when I double click this new directory, it looks like I'm in the root directory of the website but the WinSCP navigation bar shows the full path like "/public_html/20220830_setlist.html/".
Able to rename it ("normally").
Upon restoring the website from a backup (thank GOD), the glitched directory's "contents" shows the root directory with what seems like a snapshot of the broken root directory after trying to delete the glitched directory. If I try to recursively navigate to it thru itself, it throws an error "no such file or directory" attempting the second iteration.