Can't it go both ways in both languages? A messenger from the stars, or a messenger to the stars? Celestial implies that it belongs or relates to the heavens, but I don't think it strongly implies anything beyond that.
Can you rephrase your second paragraph? I'm not sure I'm understanding what you're getting at here.
I had a typo in the last paragraph that made it not make any sense...
To me, "Celestial Emissary" suggests that the creature is visiting Yharnam from the stars (in the same way that a "U.S. Ambassador" is from the U.S., instead of visiting the U.S.). Google Translate's interpretation of the Japanese name seems to think the same thing.
A while back, we were speculating that the "Celestial Emissary" could be an ascended human that the Choir was using to communicate with Ebrietas. Assuming we take the name literally and the Choir didn't just tack on "Celestial" to be showy and romantic, this seems pretty unlikely. A human communicating with Ebrietas would probably be better described as "The Yharnam Emissary to the Celestial", but "Celestial Emissary" seems to imply the opposite.
It did make me recall the "Call Beyond" description, though, which suggests that the Choir has made semi-successful attempts to reach out into the Cosmos. Perhaps that is where the Celestial Emissary came from? Perhaps one of the Choir members went out into the Cosmos, gained knowledge, ascended into an alien, and returned to Yharnam as the "Celestial Emissary"?
Or perhaps everything's just straight from space.