By 'app' I mean just a jar package, not a macOS app. So, the java process is run as java -jar agent.jar ARGS.

In fact, there is some difference between Java runtimes. I managed to get 'Files and Folders' popup only for JDK 8u181. All other Java 8 versions (latest Azul, latest Adopt, latest Oracle) just can't do that. In cases not requiring access to external drive all versions work just fine.