"If this is a New Years Eve party, should it go on the 2023 W-2, or 2024, or both?"

Never both, and technically, the next paycheck that covers the pay period in which the party falls.

"calling it a "holiday party" makes it fairly clear that this is not primarily for a business purpose"

Which is why you schedule the events to match their purpose, and the party is after the year end review and wrap up, any show and tell as to upcoming goals and projections, targets, etc. Do some business, show some graphs, then get to the fun. That's why it's called a Conference Center along with Resort or Spa or waterpark.