Self-awareness is not the same as direct reception of the absolute through intuition/gnosis which is the aim of Buddhism. Self-awareness means being involved with one's daily mental life, most notably, their thoughts, feelings, and their imagination.
Also it is a limited awareness. It only concerns the individual: the being that passed through its mother’s birth canal, to the being that will one day die.
Another way to look at self-awareness, it means understanding myself in such away that I am reasonably certain that I know who I am without being involved in a, strictly, first person perspective. Such a perspective is very much like the mystics of old who immersed themselves in the seeking of transcendent knowledge; who were also hermits.
To seek enlightenment involves first person immersion. First person immersion is not accomplished by being just self-aware, as strange as this may sound to the modern ear. It is like a deep dive into "who am I" in which one even surpasses self-awareness.
Ultimately it is accomplished by giving up even the first person perspective in a moment of absolute helplessness in which there seems to be no more path, while at the same time, absolute openness prevails. This leads to the moment of satori when, unexpectedly, Mumon's barrier 関 is transcended. Zen's mystery is solved.