Sometimes the word awareness can lead us into confusion as to what we mean by it.

If I may propose:
Rather than the word awareness, we can turn our attention to the word reality.
Via contemplation, inquiry, reflection and reasoning, we can come to the understanding of the undeniable reality of consciousness.
Consciousness is real. And there is one reality.

Concerning the world, body mind, there is no need to negate or dismiss appearance.
The non dual teaching is about the understanding that there are no external or internal realities. Both the mind as well as the world/body refer to the one reality. The reality of consciousness.
They do not have a reality of their own. They are not to be denied. We can be open to the possible existence of infinite minds and infinite worlds but not to infinite realities.

Which brings us to contemplate that the belief that there is a separate reality called me and another separate reality called the other is an error in understanding. Another error is to believe that there is a reality called me and a separate reality called the world.

Yes, there is a personal mind (and possibly many more) and yes there is a world (and possibly many more), but their reality is one.