Chapter 36 mentions that a new story will be told to quench the thirst for devotion. Is this referring to the tale of Cholkar and his spiritual welfare?

You are correct that the introduction to Chapter 36 promises a new, "succulent story" to delight the listener and remove the misery of worldly existence, thereby increasing one's thirst for devotion. The text emphasizes that listening to Sai's stories is a path to spiritual welfare. However, the material provided for Chapter 36 clarifies that this anticipated story is not about Cholkar. The chapter concludes its introductory praise by directly stating, "now listen respectfully to the most holy life story of Sai (Sai Charitra)... The Two Gentlemen from Goa," indicating that their visit is the specific narrative being presented.