Does it count as a ball hitting the referee and going into goal?

FIFA's modern football rulebook has long stated that this goal is valid as an own goal by the goalkeeper, because the referee is also an integral part of the game, of course, if it is not a part of the game, such as a bird flying into the field, a dog running into the field, a fan or an unrelated person entering the stadium and hitting the ball into the goal, it is invalid.

The referee is part of the field.

No, if the referee deliberately kicks the goal, it can't be counted.

It should be counted, but the referee who can do this kind of thing is too bad.

Count, the referee is the third goalpost.

Counting, the referee on the pitch is the same as the goalpost and corner flag stalks. If the ball hits the post, then the goal is scored against the referee.