Is the orange just a rare fruit reserved only for royal functions or is there more meaning?

It was a sort of special treat, reserved for special people at special occasions, but in the Prokofiev score, it's also an "inside joke", as the music even quotes his opera Love for Three Oranges.

Sort of like 'A morning without Orange Juice is like a day without sunshine."

One thing is for sure.
Learning this duet causes one's neck to be sore!