> How does the OS know that you moved from the "13-15" bracket to the "16-17" bracket without knowing your DoB?

The OS has the birth date. Of probably 1-5 people.

> And this is the thin edge. Because in a few years there'll be a bill saying something like "too many children are lying about their age online. We need to verify their age" and then we're capturing IDs and storing them somewhere.

Those things are already happening. I see this kind of mechanism as significantly more of an alternative to privacy invasion than an enabler of privacy invasion.