Well, we stay with birds, but besides the title and the picture this haiku isn’t really about birds. ‘Bird of happiness’ here is a hidden metaphor.
I don’t even know if such a bird exists, nor can I say for sure, if the bird in the picture is happy or not. It probably is, if it can find enough food and can avoid all predators.
Bird of happiness
Fly across the world so wide
Return for the night
The bird of happiness in this case is our soul in a happy state. During the day we should let it go, share our happiness, spirit, joy, and whatever else we can offer with the world. Or wherever and with whoever we can. (And we assume that our life is set out to be more than just a job to make money and spend the rest of the day finding ways to spend it.)
At night birds return to rest, find solace, regain their strength. And so should we. Then the next day we can ‘fly’ again.