My experience with cats is that they are definitely intelligent, in general, and are aware of a lot of things, but they generally just don't care.
One VERY unique kitten that I had, whenever he approached a mirror, or a glass door or window, would stand up on his hind legs and rapidly rub or "massage" the glass with both his front paws, like a puppy, as if trying to climb it or roll it open.
Sadly I never captured the act on camera and he died an unfairly early death that I took a long time to recover from.
In brazilian portuguese, the word "raise" (in the context of raising kids, pets, etc.) translates to "criar"; while "create" also translates to "criar".
One of our cats does the same thing with her paws, mostly on our (glass) storm door or on mirrors. She'll also do it on opaque doors when they're closed and she wants to go in the room they're blocking. Like you mentioned, maybe that behavior indicates a desire to go to the place they're pawing at.
The point is, most cats are sooo unique in personality, I think mirror only cannot give any sure about this. Without take in consideration personality and the response from another senses its hard get any reliable conclusion.
As an example, if I get food out in the kitchen while it is watching in the mirror, it comes running to check it out. Non food things - just keeps on watching.
Whether or not they know it's their own reflection I can't tell. It certainly seems like they thought it might be another cat. Perhaps they either determined there was no cat, or determined that is was just their own reflection. Either way, they don't seem to care much.
I have cared a lot of cats, and I didnt knew about all that experiences, but I did a lot about this with my pets. I put a mirror in front of the cat, and watched the reactions. The pattern is 90% the same:
1) The cat looks surprised. Depending of the the natural character of the cat, he will watch the reflex or get "armed" to fight. Cleary he think its another stranger cat.
2) The cat then try "feel" the reflex, touching sometimes, smelling other times, and ever trying look behind the mirror
3) Finally, the cat probably detects the reflex is not a threat and lose the interest
I really dont know if has some part of "self awareness", but probably the cat lose the interest really far before any of this level of perception
Other point is, the cat trust more in the sense of smell and hearing than the sense of view. Only one image is not enough to "identify" a target.