Thinking about the three purusha concept of the Gita, I was wondering if the kshara purusha can be called psychic being, since kshara purusha is a being in evolution, a being who has descended into the mutable existence. Is that correct🤔?

Kshara Purusha is everywhere in the mutable creation but the psychic being is unique to earth. The psychic being is the jiva refered to in the Gita in the verse Paraprakriti Jivabhoota. It is a portion of the Divine Mother. 

Also, how does the triple status of individual, cosmic and transcendent divine correlate to the three purushas of the Gita? Can we say kshara purusha is the individual divine, akshara purusha is the cosmic divine, and uttama purusha is the transcendent divine? I wasn’t sure of this.

Yes we can say that. 

On some reflection, I realised that kshara purusha is a “universal” being while psychic is an “individual” being. So I might be wrong in equating them. It would certainly help knowing kshara purusha and how one could make sense of it according to both Integral Yoga as well as Gita.

Kshara Purusha is the immanent Divine, the Divine Presence we feel in nature, behind its manifold phenomenon. It is due to this that one feels joy in material nature. 

Affectionately,

Alok Da