Depends on the company. A small one where everyone knows everyone else, it actually seems kinda normal.
The way large companies do it is just jarring. When my coworkers find out it's my birthday, it's because a random lady from HR is asking them which one is me so they can deliver the card.
The random lady from HR is why a previous manager sent out a message to my team wishing me a Happy Birthday. In between saying thanks to my teammates, I messaged my boss that my birthday wasn't for another month.
The way large companies do it is just jarring. When my coworkers find out it's my birthday, it's because a random lady from HR is asking them which one is me so they can deliver the card.