Following the end of the war, Sasuke is forcibly taken back to the village where he is imprisoned. The amount of time he’s imprisoned varies - a couple of months minimum to about a year - but when he’s finally pardoned, he has no desire to stay within the village. There is too much pain and trauma that lies within his place of birth and even with the people who resided there alongside him.
He knows the people don’t trust him -- whether it’s because he’s Uchiha or because of his past actions or a mix of both, there’s discomfort from being watched almost everywhere you went without respite.
So Sasuke decides to leave: not so much on a journey of ‘redemption’ as canon calls it, but more so to find himself -- to discover who he is without the hatred and trauma and need for vengeance. It’s something he’s never known, at least not since he was a child before things went so wrong. All he knows is taking the pain away... surely there has to be something more.
He does not come back to be the ‘shadow kage’ of the leaf village. While he keeps in vague contact with N.aruto, S.akura, and at times K.akashi, he’s virtually cut all ties with the village and is more or less a wanderer/traveler. Unless there isn’t any notable change made within the village and it’s structure, he refuses to come back.