Update 13 Oct 2021 iOS 15.1 (19B5042h) and 15.1 beta 3 (19B5060d):
The Screen Time API still appears to be bugged out of its mind. I am not able to consistently list the applications from the child devices on the guardian device. It worked at one point for one child device with iOS 15.1 (19B5042h), meaning I was able to see the apps from the child device on the guardian device, but in my setup I had two child devices and I wasn't able to see and list the apps from the second one. I contacted Apple DTS and this is what they had to say:
Q: How would I go about seeing and managing apps from the second device? I also tried factory resetting the second child device and re-authorizing, but the apps never showed up on the parent device, even after cold starting the app. Is there a way to choose between the devices/accounts available to manage via FamilyControls?
A: There is no way to choose. All I can suggest is try de-authorizing both child devices and the guardian device, making sure all are enrolled in the same iCloud Family, and the child accounts are under 14 years old, and both have ScreenTime enabled. Make sure the guardian device can see the child devices in ScreenTIme. Then try again. If apps from both devices still don’t show up on the guardian device, then please file a bug report with sysdiagnose logs from all devices, so our engineers have the data they need to start investigating
I submitted the bug report FB9700146 with attached sysdiagnose logs from all the devices, but I'm not optimistic about this.