Same. I still don't know the social script in these scenarios. Do I individually thank everyone for their birthday wishes? Do I thank everyone with one message after it seems like everyone's done? How long do I wait? What if someone jumps in after I do that with a belated happy birthday?
I think a simple "Thanks, everyone!" message posted sometime during the day at your convenience is sufficient; individual replies or replies to subsequent messages are not necessary.
It's uncomfortable for me too. I asked HR to keep mine private at work, but before this I would just react with a like to the wishes and write a short thatnk you all at the end of the day... The late wishes I would just ignore...
For many people it's the one day of the year they feel special. I think we all deserve that, and it costs me nothing to wish someone a happy birthday. That's not to say I'm required to spend time or money on them, but it doesn't bother me when all they want is a bit of recognition.