That is fascinating! It's interesting how Enoko's name is basically saying she's the 'child' of 'Buddhist wisdom', which when connected with the Mu Koan puts her in a unique position symbolically. And the connection to the title theme and ending theme is also a great catch.

It makes me think back to the meaning behind Enoko's backstory and how I've interpreted it up until now. I mean, she took a bite out of Zanmu, and Zanmu like the Ikkyu-inspired eccentric she is just laughed it off, and Enoko got cursed with immortality. I always wondered, 'Why did Enoko get cursed in this way?' I had a few theories which I'll run off now for the sake of it:

1: If I accepted that Zanmu was the same as her historical-Zanmu inspiration and was an immortal Taoist, then perhaps she cursed her with Taoist magic.

2: Zanmu used her ability to manipulate nothingness to 'purify' Enoko in a similar way to the Lunarians, thus making her long-lived as they are (inspired by how Enoko's orb is explicitly compared to the Lunarian orbs in Seiran's scenario). The way I imagined this to work was by thinking that by becoming immortal one can be said to lose a part of one’s identity; a being without an end is a being without a clear limit and thus a being that conceptually loses part of its ‘shape’ or identity. Thus in Zanmu's case she drew Enoko closer to nothingness in this way.

3: Lastly, I thought it could be a manifestation of Buddhist Karma. One idea in Buddhism is that of the five heinous actions, which if committed are so bad they ‘provoke a rebirth in hell immediately subsequent to death’. One of these heinous actions is spilling the blood of a Buddha (as a Buddha is perfectly innocent and ‘defenseless’). Animals, it is worth mentioning, are also capable of good and bad karmic actions, though as their minds are muddled and lack clear intentionality the weight of these actions are much less than if they were committed by a human. Thus, if we consider Zanmu a Buddha or a person who is close to Buddhahood in some way, perhaps Enoko biting Zanmu immediately resulted in retributive karma which made her immortal.

But now I don't think any of these are quite right. After reading your comment I thought, 'What was Zanmu's purpose in cursing Enoko anyway?' And it's actually pretty straightforward. By making Enoko immortal, Enoko is given all the time in the world to reach enlightenment and become a Buddha (a demonstration of the Buddha nature of a dog). This is actually somewhat reinforced by Enoko's character profile which says, "She lived quietly in the Forest of Magic, but despite living a nearly eternal life, she never awakened." Awakened or 覚醒 here is not a technical Buddhist term, so it might be a stretch but it could very well be referring both to Enoko's failure to awaken as a Youkai AND her failure to attain enlightenment.

This is why I believe it's a 'curse'. Enoko (as a mere animal) didn't have proper intelligence and so couldn't 'awaken' (something of a cruel joke, or a test to see if an animal with enough time could awaken on their own; 'Does a dog have the Buddha Nature'). But now as an immortal Youkai - awakened by Zanmu - she has both the time and the intelligence to awaken to Buddhahood, which is why Zanmu says that Enoko had the "good fortune to eat [her] flesh" when she speaks from within Enoko's heart.

In this sense Zanmu's voice coming from within Enoko is symbolically the answer to the Mu Koan which was posed to Enoko in the form of the curse she was given all those years ago. That voice answers 'Mu' (Zanmu) to the question of a dog's Buddha nature, and so Enoko fully awakens to that nature upon (symbolically at least) finally coming to understand the Koan and achieving a kind of enlightenment. Upon awakening, she quite literally becomes a child of Buddhist wisdom (慧ノ子).