Currently the account wide essence vendor MOTHER in the chamber of heart is not allowing this character (or any other) to buy essences of which I have met the requirement.
In the case of the Essence I specifically wish to buy, it is Blood of the Enemy.
There is the PvP vendor in Zuldazar/Tiragarde Sound that sells you the rank 2 and 3 essence after you complete the prerequisite quest to earn rank 1 and earn the achievements in order to buy the others. (Which one of my characters, Cecile-Kazzak has done and has obtainted the rank 1, 2 and 3 Essence.)
And then there is the account wide Essence vendor, MOTHER, that sells the Rank 3 Essences for alts and has as a requirement in red text at the vendor that you need to have obtainted the Essence on rank 3 on another character. (The one that I bought from the PvP vendor and earned the achievements for on Cecile-Kazzak.)
Sadly, it seems that even Cecile can not access the rank 3 Essence here despite literally using it in her Heart of Azeroth.
And I farmed the Echoes of Ny’alotha currency to buy it on this character from MOTHER where I also get told I don’t have a rank 3 Essence of Blood of the Enemy on my character.
I would gladly move on and just re obtain it on this character (which I use for timewalking, hence the essence farming), but the initial quest to obtain rank 1 requires you to win a PvP island expedition, something nobody queues for in Shadowlands.
Thank your for bring the attention of this to the forums, I am player Sindekiveth and I shall assist you throughout this adventure.
I understand that you have recently unlocked the rank 3 Chruning Blood of the Conquered Azerite Essence and would like to purchase it from MOTHER with another character but are unable to do so and would like the essence unlocked on Tsuzaki.
I can perfectly imagine that not being able to purchase the essence on another character, after so many efforts, might feel a bit frustrating but have no worries as player Sindekiveth has come to shed some light upon this matter.
After having thoroughly investigated the issue and thanks to my Great Mystical Powers, I was able to determine that each character has to complete the achievement criteria before they’re eligible to purchase the azerite essence.
Here’s an old parchment that I have found on one of our dusty bookshelves confirming this important information:
Game Masters are unable to unlock essences for other characters at this point.
I can imagine, oh dear Tsuzaki, that this may not be the answer that you were hoping for, but I would like to thank you for your patience and understanding.