They're not really for many people (and, personally, I don't go to any extremes to keep it a secret). But sharing info like that from an HR record without permission feels a bit wrong even if others here obviously disagree.

It depends on the culture/religion. Not everyone celebrates birthdays.

I had multiple ICs ask me not to say public birthday wishes, as they didn’t celebrate their birthday and/or did not want the rest of the team to know.

They should be unless you want to publish one of the things that too many (eg sites) regard as a reasonable secondary security verifier.