Is not the awareness of our thoughts and emotions important?

While there is psychological suffering, doubt and seeking, yes. Because by acknowledging what is false to be false it gets discarded naturally by consciousness itself, and thus the suffering, doubt and seeking that the false produces cease to be experienced.

Awakening engenders a change of perspective to the experience of self. The Self itself, that is our True Nature, does not change.

Eventually, the concept of self-awareness as “the experience of being aware of one’s thoughts, emotions sensations and surroundings” lose all spiritual meaning or value.

To Spirit, being or not being aware of the universe has no importance or relevance whatsoever. In fact, being or not being, and the entire duality that cascades from being, has no intrinsic value.

What a relief. Normalcy.

So you have a disregard for everything?

On the contrary, all becomes an expression of truth, love and beauty. But there is no illusion of permanence or fear of loss or dissolution.

Nonduality, Advaita. The end of suffering.