What does "happy" new year actually mean?

“Happy New Year!”

Thank you, but if I may riff on Gandalf at the beginning of J.R.R. Tolkien’s The Hobbit, do you mean I should be happy in the new year or that we should be happy that it is a new year or that you are happy it is a new year or that the new year will be happy? If you’re greeting my arrival, do you mean, “Hello”? And if I’m leaving, do you mean “Goodbye” only with a seasonal flair?

And what exactly constitutes a “happy” year? Was 2022 a happy old year? What would make 2023 a happy new one?

It all depends on what “happy” means.