As the coronavirus subsided in New York last year, Gov. Andrew M. Cuomo had begun pitching a book proposal that would center on his image as a hero of the pandemic. But by early last summer, both his book and image had hit a critical juncture. Mr. Cuomo leaned on his top aide, Melissa DeRosa, for assistance. She attended video meetings with publishers, and helped him edit early drafts of the book. But there was also another, more pressing edit underway at the same time.