The dream within the dream is your thinking about what is Essential and what is non-essential, and when you realize that you are the Self, Atman, then you have this experience...
You felt that the world is illusory. You felt that you are awake and that it is your waking state. You felt that you have obtained 'experience,' but still, your confusion, your illusion, is persisting as it was. You are yet talking about things in the dream.
When there is true awakening, all the sense of 'being' disappears. Even the sense that you are the Self, also dissolves.