A collection of entities or the pattern the entities partake in are NOT self aware. It's only the entity itself observing the pattern or collection as such, that is.
It seems people are postulating properties of collections and patterns of groups, then checking things off, one by one, being satisfied of the similarities. It is the person checking these things off that is realizing similarities then taking the leap of anthropomorphizing awareness into that idea.
The salient difference for me here is that the brain has a holistic factor:
Individual brain cells are not self-aware, or intelligent in any capacity. A whole brain is both.
Individual humans in The United States are aware of both themselves and of the United States. The United States is arguably not aware of itself in a greater-than-the-sum-of-its-parts capacity, as a human brain is.
(So far I've only read the abstract of the linked article)
It's a fun thought experiment, but the illusion of self probably didn't just spontaneously arise in humans; it's much more likely to be an adaptation from hundreds of thousands of generations of natural selection for a more intelligent species. Nature selected countless times, through genetic succession, for the more aware species.
> do you think that brain cells are (would be) aware of the fact that we are conscious?
No, a neuron is too simple a system to be capable of awareness by itself. I get what you're getting at, but if we're talking about a higher-level phenomenon, let's not also call it consciousness. In fact, we essentially use "consciousness" as a post-facto description of our own illusion of self, so it essentially makes no sense to ascribe it to a system that didn't arise more or less the same way as we did.
It seems people are postulating properties of collections and patterns of groups, then checking things off, one by one, being satisfied of the similarities. It is the person checking these things off that is realizing similarities then taking the leap of anthropomorphizing awareness into that idea.