Identity and transcendence are hard things to talk about, they mess with the English language in weird ways. One person’s identity-removing experience is bound to be different from the next person’s. And transcendence is when a thing and its contradiction are shown to both be true.
Enlightened people are both non-existent, in that their selves play no direct role in whatever goes on around them, and are also extremely present, in that the lack of self to get in the way means you feel an immense sense of presence just being around them.
The contradiction is key to deep understanding of the state. Language is how the mind makes sense of the world. But the mind is trying to transcend itself, so using language as a tool, by insisting that conflicts be resolvable, that the state of enlightenment is understandable, that everything ‘makes sense’, is a huge obstacle to actually arriving there.
The conflict you’re referring to is this need for rationality. When you no longer need everything to make sense, that’s when the inner conflict is resolved and you become enlightened. Not needing things to make sense, you no longer need appellations that are intended to make understandable things that we are functionally incapable of understanding.
This doesn’t mean you completely throw rationality out of the window. It just means you don’t incessantly need to understand everything. You understand that which can be understood, and realize that your understanding is of necessity flawed, perhaps in ways that make it completely broken, and you’re fine with that.
You cannot be enlightened while still holding on to belief in the self.