The goalkeeper caught the ball and passed it to the defender, who mistook it for a goal and touched the ball at tee time. How to punish? Is it a penalty or a direct free kick in the penalty area?

According to the meaning in the question, the defender should touch the ball with his hand in his own restricted area. In this case, the referee should award a penalty for the following reasons: the goalkeeper catches the ball and passes it to the defender. It's not a dead ball at this time, so the game is still going on. The defender mistakenly thought that the handball touched the ball when kicking off. Obviously, this is the subjective misunderstanding of the defender. Football rules don't say that players (except goalkeepers) don't have to be punished for misunderstanding handball in their own restricted area, do they? Therefore, according to the rules, because the non-goalkeeper player deliberately handball in his own restricted area, the opponent should be awarded a penalty.