Free will and unified consciousness

Hello, Your Honor,
I watched a lecture on the meaning and place of free will, and now I understand why proving the non-existence of free will, given the possibility of actions without a cause, but with a purpose (or purpose), is impossible.
But I have a question about the nature of these actions. I am willing to accept the fact that they have no cause, even though it is no more intuitive than absolute randomness, since I have no way of contradicting it, so it is indeed a possibility.
My question is about the purpose of the actions; I will assume that there is no unified consciousness (this is not the topic I would like to discuss right now, but if it needs to be discussed in order to answer the question, I would be happy to (: ) (What I mean by unified consciousness is that there is no one particular thing, like a soul, that can be said to be you; human consciousness has no place where it unites, but consciousness is the collection of all the things that make it up, and their union is a kind of illusion.).
On this assumption, where would the purpose for free will come from? According to my understanding, the purpose for actions that come from free will must be consistent, because if it is inconsistent, and has no causes, then it is random, and we say that free will is not random.
So if the purpose is consistent, and it differs from person to person, then there is a need for something, which is the person, who in a certain way will contain the purpose and act according to it.
To sum up all the swans, my question is this: In your opinion, is free will still possible in a worldview that denies the existence of a unified consciousness? And in such a case, is the question of free will even relevant?
Thank you very much,
colleague.