The page ≪https://aboutme.google.com/ ≫:
When I click on the lock icon beside "Birthday", it's this:
Yet when I click on the edit button, it shows:
So is the account's birth year shown or hidden to the public?
Nobody can see your "About Me" page but you. You'd need to look at your public profile.
If you go to https://profiles.google.com/me when you're logged in, it will redirect to your "public" Google profile (whether that's Google+ or not). Visit that same URL from an incognito browser tab and you'll see what other people can see.