The privacy implications for this bill for adults seem to be about the same as the privacy implications for the "Click if you are 18+" button on many websites.

If you are under 18 there is no checking to stop you from saying you are are 18+

The only people it seems might have their privacy slightly reduced are people under 18 who are using a computer or smartphone/tablet that had parental controls set up by presumably a parent or guardian before giving the minor access.

The bill requires that the parent be able to enter the minor's birthday or age in one place, and then provide a way that the age range (under 5, 5-10, 10-13, 13-16, 16-18, 18+) can be given to apps/sites if they ask for it.

Thus, if you are a minor using a device that was set up with parental controls and you try to use an app or site that is restricted, that app or site will find out your age range.