Is the dialogue mentioned in the question considered an affirmation of divorce, and is it explicit or implicit, knowing that no breaking of an oath was mentioned, and that he had previously informed them of his wife's anger while she was with her family?

The statement mentioned in the question is not an affirmation of divorce, as it is merely a compliance with obsessive thoughts, a yielding to them, and based on possibilities and illusions that do not exist, since the husband did not swear an oath. Rather, he made comments using allusive (kinayah) terms. Therefore, the questioner should avoid delving deeply into issues so that it does not lead him to obsessive doubts; for excessive questioning is blameworthy in Islamic law, and it wastes the time of both the questioner and the one being asked.