What are the "Esoteric Teachings" Emma wants me to learn?

Solution 1:

"Mastering Esoteric Teachings" refers to learning last skill in skill tree. This is condition to get Mushin Esoteric Text from Isshin or Tengu of Ashina, unlocking Mushin skills tree.

Emma implies, that player can obtain Mushin Esoteric Text from her, if he didn't managed to obtain it before Isshin has died.

I'm not sure, why this phrase appears even if player already got Mushin Esoteric Text.

Solution 2:

TLDR: It's a bug, you're not missing anything

It's a bug in the game with how quest lines are interacting with key items.

I'm going to assume this is NOT your first playthrough.

SPOILERS AHEAD

The Mushin Esoteric text is granted to you by the NPC Tengu of Ashina, which if you pay attention to the back wall and assorted other lore bits, will inform you that Tengu was actually Isshin Ashina the whole time! However, once you progress to a non-Shura ending, after defeating the Divine Dragon, Isshin Ashina dies.

If you had started his questline but never fully mastered a skill tree prior to his demise (so on your first playthrough) then you would forever be cut off from getting this skill tree. To compensate, Isshin gives the text to Emma before his death with instructions to only pass it on to you once you've fully mastered another skill tree.

But... well, NG+ throws all that off. Its entirely possible you talked to Tengu once just because he was around, but never hunted him down to 'finish' his questline. However, since it started, its trying to provide you access to finish this quest still. And unlike other instances in the game where you just get a 'duplicate' esoteric text that does nothing as far as I can tell, this one is bugged and just blocks you from ever receiving it. You can't hold more than 1 of a key item by standard code (from my experience)