I noticed the Shri Sai Satcharita has 53 chapters, but I heard it was planned differently. Can you explain the story behind the final chapters?

Your observation is correct, and the reason for this is explained in Chapter 0. The author, Annasaheb, had originally intended for Chapter 52 to contain a summary (Simhavalokan) and a conclusion (Avataranika) for the entire work. However, he had a habit of writing verses on loose slips of paper. It is believed that the specific slips containing this concluding material for Chapter 52 were lost before the book's final compilation. To provide a proper ending to the scripture, a new concluding chapter was prepared and added as the 53rd chapter, completing the overall structure of the book as we know it today.