I must have missed the memo stating that the new Astrologian job is the Sharlayan version of the more familiar one we currently see at the Observatorium.

Thanks for the information, though! I've always felt it strange that the city-states don't have their own guilds for each class. It's one thing to associate lancers and archers with Gridania, musketeers and marauders with Limsa Lominsa, and gladiators and pugilists with Ul'dah, but quite another to have just "one" guild for each profession based in just
one city.
It makes it appear as though any foreign practitioner of that discipline would have to travel to that city to learn the craft. Of course, I don't think it's actually that straightforward — the Archons apparently mastered their professions in Sharlayan, so it suggests that, in Sharlayan at least, there are traditions which are separate from those of other city-states.
For example, I don't think Y'shtola is beholden to the elementals of the Twelveswood, despite ostensibly being a conjurer.