Only sa yo u na ra can also be said to be sa yo na ra.
This has nothing to do with English.
On the contrary, many people who don't know Japanese think this is the English word see you, but they mispronounce it.
さよぅなら, literally translated as "in that case". Japanese is euphemistic, but this sentence actually omits the second half of the sentence "don't". In that case, let's break up. This sa yo u na ra emphasizes "bye-bye" rather than "goodbye" in meaning, even a little close to farewell, which is completely different from the English word "see you". See you in English means じゃjia, which means "then". Omitted またぁしたたたたたたたたたたたたたた.