The phrase John used here, "to prosper in every way and be in good health" was a common phrase in everyday language at the time. It was so common for people to use this phrase that when writing it in letters, people didn't even need to write it out but just used shorthand, writing the Latin abbreviation of the phrase instead. No need to expound, they knew what you meant. Just like when some sneezes, the "bless you" comes almost as a reflex.

Oh but what stuck out to me is that John is not just wishing his friend Gaius good health and to prosper, as was the custom, but he tied it to the health and prospering of his SOUL. Some versions say "As your soul prospers".