What class are you talking about?
I can only speculate that you are reading something about Dark Knight, Machinist, or Astrologian ... which require you to have finished that quest. But only in the sense that their class trainers are located in Ishgard. And that you can't enter Ishgard without having finished that quest.
But looking at your Lodestone ... you HAVE unlocked Astrologian, and are up to Endwalker in the MSQ, so ... I'm stumped on what you mean.

(Also, don't bump ancient threads, even if they sound super relevant.)