Is an expiation (kaffarah) for breaking an oath (yamin) obligatory upon someone who swore not to masturbate for three months, then had a wet dream, woke up while semen was discharging, and then performed an action that caused the semen to be expelled?

The questioner mentioned that he swore not to return to masturbation. It appears that what happened to him was not actual masturbation, because he had a wet dream and experienced arousal without intending it; he did not initiate it from the outset. Yes, he did something that prolonged the pleasure and hastened the expulsion of semen, but this is not precisely what he swore to abandon. The intention of the swearer is what matters, if he intended something that his words could bear, based on the Prophet's ﷺ saying: "Actions are but by intentions, and every man shall have but what he intended." Thus, the swearer's intention specifies and restricts his oath. Based on this, he does not owe expiation.