For anyone who doesn’t know that’s Cockney rhyming slang. Cup of Rosy Lee rhymes with Cup of Tea. But they often omit the last word so it becomes a Cup of Rosy.
Another one is Apples which is slang for stairs. Since the full rhyming slang is Apples and Pears.
It isn't that Joe is short for something coffee related, it's that it's short for Joseph, whereas James is just short for James
Afaik, like you said, joe as in coffee doesn't have a confirmed etymology. I tend to think the jamoke origin is most likely, though I've known a few Navy vets of the era claim up and down that that's the origin that's true (the Josephus Daniels alcohol ban story). I sure wouldn't disagree that that's where they ran into the term, but it isn't definitive either.