I have the exact same question. The correct passcode to ask for when authorizing an app to manage the Screen Time settings should be the Screen Time passcode, not the device passcode or Face ID.
The reason is pretty simple. If you want to use Screen Time for your own device, you need a way to lock the Screen Time settings with a passcode that you don't have memorized. You can write it down, or give it to a friend, so you yourself won't easily be able to change the Screen Time settings (for example, when a time limit is used up).
The same goes for locking an app that manages Screen Time settings for you using the new requestAuthorization(for: .individual) API. There ought to be a passcode, separate from the device passcode or Face ID, for locking in one of these apps that uses the new API. It would make the most sense for that to simply be the Screen Time passcode.