Unless the ATO wants you to play a Descent-style game to navigate their bureaucracy?
If it is a Java app, it should be easier to decompile and inspect.
I downloaded the dmg and extracted the contents, it's a launcher for a JavaFX application with a bundled JRE 8.
The java code isn't obfuscated, and I don't see anything particularly interesting, but it would require going through a lot of code.
However, the build and file modification dates are all 2017, which is pre-Catalina. Catalina of course introduced this permission warning.
I instead did a quick Google for JRE bugs with this issue and it didn't take long to find this issue raised with OpenJDK: https://bugs.openjdk.java.net/browse/JDK-8231513
In particular, this comment: https://bugs.openjdk.java.net/browse/JDK-8231513?focusedComm... explains it's to do with mouse tracking around window resizing.