I think this is a bit confused. The idea of an Unchanged Changer is that the Changer is Unchanged by anything outside of itself. All other changed entities MUST rely on something else to effect change in them - to that extent they are dependent or contingent and do not, in themselves, explain changes that occur to them or have any “power” within themselves to effect change. They rely on other entities for their power to effect any changes. They are changed changers, and effect change on others BECAUSE they themselves are changed. Thus the batter’s arms rely on signals from the brain which rely on energy from the digestive system, which relies on food coming into the system, which relies on energy exchange in nature, etc. etc. until, as Aquinas pointed out, we end up, logically, at the Source of all change.
The point is that God, AKA the Unchanged Changer, can effect all change without reliance on anything else - i.e., Unchanged by anything outside the nature of God who is, by definition the fullness of all existence, the source of all that exists. In vernacular speak: Being where all the bucks stop and start, if you have the wherewithal to follow the bucks to their origin and destination. It is God alone, ipsum esse subsistens, that explains his own existence and the existence of everything else.
The idea of an Unchanged Changer is that all change is sourced within the essential nature of the Unchanged Changer - which is the completeness or fullness of all actuality and CANNOT become or change into something else purely and logically because there is no lack, no potentiality, nothing unactualized in the Unchanged Changer - who is self-sufficient, which is to say omnipotent. Nothing can change because there is nothing left to change, nothing left unactualized - Aquinas’ definition of Actus Purus: Fullness or effulgence of Being, from which all change derives.