Can the AI group the chapters of a new book into parts for me?

Yes, from version 1.9.24. In New Book, on the Structure step, find "Group chapters into parts", under "Review the outline first". "Off" writes one run of chapters, as always (you can still add parts later). "Let the AI decide" lets the outline group related chapters into parts when the book reads better that way; it only applies to books of 12 chapters or more. "On" always groups them. The outline then proposes the parts, and each chapter is written knowing which part it belongs to. The option is not shown for a collection of separate stories, or for a book planned with "Plan my book with me" whose chapters are already agreed.