If you wish to affirm that many species are self-aware, I will grant that provisionally. My contention is that consciousness has to be a threshold and not a continuum. The reason is that it is not possible for a being to be aware of something else but not aware of itself. And once you are aware of yourself you are aware that there is an environment outside of the "me." You are able to separate the "me" from the not-me. Indeed, you might be confused about whether your paws, say, are part of your body or not, but that makes no difference. What you are aware of is your "self," not necessarily your body. You may not know what any of these things are outside the self--it makes no difference for full consciousness to be. So dogs could have self-awareness and still not recognize the figure in the mirror, but the reason is that they don't know what mirrors do, not that they don't have a sense of self.
But what is it that this being of whatever species can do if he has self-awareness? All sorts of things. For example, he can remember (indeed, without memory there would be no sense of self). But not only that. If he can remember he has a sense of time and if he has a sense of time he can visualize the future and know that that is what he's doing. Self-awareness opens all mental doors. That is why consciousness is a threshold.
But since we cannot look into a dog's mind to know for sure what is going in there, we can ask ourselves, looking from the outside, what is that animals lack that humans have that creates the vast differences in their abilities? The answer is language, by which I mean the ability create sentences you have never heard before. My contention here is that language is dependent on self-awareness.