What is the "heart" intended in Allah's saying: "He comes in between a person and his heart"? And is the heart the core of the self or the soul?

The heart is a creation, not the soul. The soul is a divine subtlety connected to the physical heart, and the heart is the essence of the human being that perceives, is addressed, and is held accountable. The physical heart is a fleshy organ on the left side of the chest. As for the spiritual heart, it is a divine subtlety connected to this physical heart; it is the essence of the human being that perceives, knows, is addressed, is punished, and is held accountable. Scholars have differentiated between the heart and the soul. The term 'heart' is used for both the fleshy organ and the divine subtlety, whereas the soul is a subtle body emanating from the cavity of the physical heart and spreading throughout the body. Meanwhile, the term 'self' (nafs) refers to the essence of the human being or the comprehensive meaning of the powers of anger and desire within it.