Honestly, I don't know exactly what google can or can't track if the app developer doesn't specifically enable them. I don't have specific evidence that they'll even be able to tell if the user was verified or not

What I do know is they have repeatedly shown that they're happy to hide or lie about what and how they track people, and more broadly about their business as a whole.

Again I cite the drug analogy. Google is in the business of tracking people and harvesting data for ads. It's like inviting the cartel to the DARE program and expecting everything to go swimmingly.

If they want their age verification app to actually be anonymous, they shouldn't force people to use a tracking service to use it. The app specifically won't be functional on degoogled android phones and won't be offered on desktop computers. Maybe Google can't spy on anything going on in the app, but even so, they could correlate "used verification app, roblox usage went up" or "used verification app, continued to use Tinder, concluded adult, ignoring 'do not track' preference as it doesn't violate laws about tracking minors".

It's true that a minority of users have taken the steps where this inferred information would be particularly helpful to google, but not having the option to opt out is going to get harder and harder, and this service doesn't provide enough good to give the information cartel that is Google any more information, even inferred, in my opinion.