Well, the API itself seems fairly well designed from a privacy perspective. It only shares age ranges, not specific ages, and only if you allow it. The data is also fuzzed to prevent an app from determining your exact birth date, and it's all tied in to the parental control system.[1]
The problem remains though that, since the laws this feature was created to comply with put the onus on Google to verify the user's age and not on the device owner (e.g. the parents), the method they use to determine the user's age to feed into this API is terrible from both a privacy and freedom perspective: they force you to send them a copy of your government ID, and delete your account if you don't comply.[3]
[1]: https://support.google.com/googleplay/answer/17232873
[2]: https://developer.android.com/google/play/age-signals/unders...
Look, it's just a start. Up next: KYC via Persona to use your phone.
This is kind of inevitable.
The API is tied to a Google account though. You can't simply install an app on Android and have Android tell it what the user's age is, it has to first have google maps, youtube, play services, etc. installed and you need to make an account and log in globally on your device before it can tell the app an age. I don't know that I'd call that a good design for an Android API