Is wishing someone happy birthday in a work newsletter a breach of privacy?

If the person has told lots of people in the workplace about their birthday and the newsletter is only circulated within the workplace then it is not a problem. But you should not search employment records to find out colleagues’ birthdays for this purpose because that is not why the information was collected.

Try thinking about the culture of the workplace and about the person involved. Considerations of courtesy are a good guide. If publishing a colleague’s birthday is going to embarrass them in some way, or oblige them to provide a shout when they don’t have the time or money to do so, then don’t do it.