Yep. It's Great Gubal Library (Hard) that you're missing, not Great Gubal Library.
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It's a level 59 dungeon, that's the normal difficulty,
(hard) would literally say (hard) and is level 60
Then why does the aether currents say the quest is incomplete?
It's probably a different quest that you're missing.
Quest Level Coordinates
Louder than Words 58 (x21, y18) Unlocks after completing Heavensward MSQ Main Scenario QuestA Great New Nation
Ebb and Aetherflow 58 Idyllshire (x7, y6) Unlocks after completing Heavensward MSQ Main Scenario QuestAn Illuminati Incident
Taking Stock 58 Idyllshire (x5, y6) Unlocks after completing Heavensward MSQ Main Scenario QuestLeaving Idyllshire
Saro Roggo's Common Life 59 Matoya's Cave (x6, y6) Unlocks after completing Heavensward MSQ Main Scenario QuestMatoya's Cave
https://i.ibb.co/DKJDRC2/ffxiv-06252024-155308-315.png
Clicking on it does not go to a dungeon so I was wong.
So that is probably the "Ebb and Aetherflow" quest available to you in Idyllshire at (8,7). Halfsix offers 2 quests, so if the map doesnt indicate this one talk to her and you should be able to choose it.