How sound is the attribution of the popular story about Imam Al-Shafi'i, in which he uses the mulberry leaf and the variation of its outputs based on those who consume it (silkworm, bee, deer) as evidence for the existence of God?

The story mentioned and what is attributed therein to Imam Al-Shafi'i cannot be judged as authentic or weak. However, it is widespread among students of knowledge and the general public, and it has been recorded by Ibn Kathir, Al-Qarafi, and other scholars in their books. The fact that these great scholars mentioned it and that people have widely transmitted it makes it closer to authenticity, even if they did not mention a chain of transmission for it. This type of story may reach the level of moral tawatur (recurrent narration).