I grew up with wild and domesticated animals. The animals I knew were very mindful of social status, predators, food, shelter, the weather, routines, they all had different personalities and complex forms of communication. They use scent, body position and vocal sounds to communicate and in a way growing up with them I learned their language and they learned mine, except they couldn't speak English
Most of my animal friends knew far more about what was going on with me then I knew about them because they could smell my feelings before I could think about my feelings.
Animals are mindful of all these things to do with their life because they can easily die and are very alert about staying alive. An example a squirrel is very mindful where it is stashed it cache of nuts. I don't see my animal friends going through the anxiety of identity unless they have been abused. Then they act very much like human beings. Throughout my childhood and as an adult we took in abused horses and dogs, especially old ones.
Whether they are mindful of their Buddha Nature, I'm not a Buddha so I wouldn't know.