I have Luna Nguyen's book too. It's the first thing you said and that includes the second. They speak about consciousness in the classical, narrow, individual, sense in the beginning and transition to a broader meaning later. This makes sense, as they move to a different level of abstraction and explain how consciousness is situated in and arises from a material world and society.
Narrow start: p. 64:
Consciousness is an attribute of a highly organized form of matter, which is the brain. Consciousness is the function and the result of the neuropsychological activities of human brains. As human brains evolved and developed over time, their neuropsychological activities became richer, and, as the activities progressed, consciousness developed further and further over time.
This is the classical meaning of consciousness as an inner experience that reflects the world.
p. 79:
However consciousness does not perfectly reflect the objective world. It modified information through the subjective lenses (thoughts, feelings, aspirations, experiences knowledge, needs, etc.)
Here it gets a little broader.
p. 80:
Consciousness is a social phenomenon and has a social nature. Consciousness arose from real life activities. Consciousness is always ruled by natural law and social law.
That's broader still, but it logically follows from the first material definition.
You say
I don’t see how the experience of consciousness can affect matter.
The answer is on page 88:
The relationship between matter and consciousness is dialectical. In this relationship, matter comes first, and matter is the source of consciousness; it decides consciousness. However, consciousness is not totally passive, it can impact back to matter through the practical activities of human beings.
(Emphasis mine) That's an even broader level of abstraction, the dialectic is revealed.
Later in part 1 they explain the difference between ordinary and scientific consciousness which is a narrower application of the earlier term that leans more into the second definition you gave. But it arises from the earlier one.
And in part 2 they explain how you get class consciousness from that.
(I said Luna Nguyen's book, but really it's a work of many authors. Luna contributed the translation, annotation and illustration)