Is not the soul on a path through many lifetimes and it evolves that way?
Yes, metaphysical insight or deep intuition reveals that to be the case.
Just like the body and personality change and evolve in their own way during this physical life, the soul, or a metaphysical body, evolves through multiple lifetimes and then later without a physical body. Nisargadatta Maharaj refers to these experiences as “consciousness” with lower case “c”. It is the “manifested”.
But in my view seeking spiritual realization has no concern with the evolution of the soul. In fact, such concern becomes an obstacle. Any concern with “me”, whether it is “me” personality, “me” body or “me” soul, is an obstacle for the simple reason that there is no such “me” to be found. Thus that concern is imaginary.
If we persist in asserting the existence of “me” then it is suggested to look again. If that does not work then we have to backtrack and study the personality’s mechanism of suffering in order to recognize in direct experience its components and how they operate. And then, by recognizing the falseness of its beliefs and assumptions realize our Freedom from them.