Every ADB connection has some kind of certificate / key that is saved locally. This means that a new application would have a different certificate. That certificate is shown in the yes/no prompt.
> Does that mean that a Shizuku-enabled app would prompt the user again for ADB access any time it's started?
You can tell android to remember that certificate and allow the connection next time. There is a bug that make it not work on certains specific version of Android 12 I think, but outside of that, it always works.