Doesn't the act of notifying >16 today and >18 tomorrow leak birthdates?

Not unless you actually meant 16<x<18 today and >18 tomorrow.

You can be 30 and verify >16 today and >18 tomorrow, obviously without being 18.

which is nothing in comparison to leaking all of personal information

you can also introduce some jitter like changing age range only once a week/month/year for everyone

Birthday, zip code and gender is enough to uniquely identify most Americans.

Well don't reveal your birthday then. Wait 5 days to confirm >18.

If you run into a liquor store yelling "Im finally 18, here's proof." that's on you?

If you want privacy you need to fuzz the transition. Many platforms support that today. Or you can create a separate account when you graduate.

But also, knowing someone's birthday without trying it to other information greatly reduces the risk of harm.