The quick fix was a simple, empty index.html file (or setting the -Indexes option in the apache config). The surgeon had no idea what this meant or why it was important. And the AI bots didn't either.
The odd part of this to me was that the AI had made good choices (strong password hashes, reasonable DB schema, etc.) and the app itself worked well. Honestly, it was impressive. But at the same time, they made some very basic deployment/security mistakes that were trivial. They just needed a bit of guidance from an experienced devops security guy to make it Internet worthy, but no one bothered to do that.
Edit: I do not recommend backing up web apps on the web server itself. That's another basic mistake. But they (or the AI) decided to do that and no one with experience was consulted.