Is the death of my brother, who was taking antidepressant medication and died alone in his home, considered a suicide in Islamic law, and what is the religious ruling on his action, especially since he was a good person and maintained some of his prayers?

One should have a good opinion of the deceased, for death comes suddenly, and what was mentioned is not evidence of suicide. Even if we assume he committed suicide while in a coma or driven by his psychological state, he will not be held accountable. One must avoid discussing the matter with people, so that no ill-will is harbored against him or that he is spoken of unjustly, due to the Almighty's saying: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin," and due to the Prophet's (peace and blessings be upon him) saying: "Beware of suspicion, for suspicion is the most untruthful of speech," and "Do not mention your deceased except with good."