(NB, I don't know where I saw it but if you look at <https://en.wikipedia.org/wiki/Mirror_test#Mammals_3> about pigs: "Pigs can use visual information seen in a mirror to find food" - someone recently found dogs doing the same; finding hidden food with mirrors with distinctly better than chance).
Understanding that a reflection is a reflection isn't full self-awareness, which itself is a blanket term. Being aware of your physical presence doesn't necessitate having a sense of self.
Seeing the reflecton and recognizing what you're seeing is your own reflection (demonstrating this knowledge by fixing your hair, which you notice is ruffled) is basically the full mirror test which is the best test we have for self-recognition.
(NB, I don't know where I saw it but if you look at <https://en.wikipedia.org/wiki/Mirror_test#Mammals_3> about pigs: "Pigs can use visual information seen in a mirror to find food" - someone recently found dogs doing the same; finding hidden food with mirrors with distinctly better than chance).