I don’t see any signs of bad parenting here, but a lot of signs of carrying on of a suicidal conversation by ChatGPT indeed, to the point of encouraging the suicide.
You theoretically could blame bad parenting if the parent monopolized the time of the child to near 100% of their life. But, that isn't the case in our world today. Society, and the circle of people around, are most of the influence that shape the child's sense of reality.