The article's definition of consciousness is precise, but it's not what people are referring to in most cases where the word "consciousness" is used. Of course, a word can have multiple definitions. But colloquially, when people say consciousness, we usually mean the thing that goes away when we sleep or are anesthetized. I don't think there's a much better way to define that. The contrast between the wakeful and non-wakeful state as oneself experiences from the inside is precisely what defines consciousness in the colloquial sense. It seems to be a self-defining concept because I can't even define what "experiences" means without thinking about the wakeful/non-wakeful contrast phenomena that is consciousness, and "experiences" was supposed to be a part of the definition of "consciousness" one sentence ago.

I am unsure as to what you are trying to say here. It reads to me as “the word the article discusses has a more popular homonym, but they are clearly not talking about that”.

Anesthesia is a rather different state than sleep.

The more interesting aspect of that is that there's an element of recall implicit in that though: if someone was active, moving around and interacting according to observers then whether they were conscious during that time is heavily informed by whether they remember it later.

Quite where that line exists then is very fuzzy because while for example I feel conscious while I'm typing this, it's also clearly possible I could but then have no memory of it.