Can I write my book with ChatGPT (OpenAI) models?

Yes, from version 1.9.16. Open Settings, stay on the "AI engines" section and click "OpenAI" in the row of engines. Paste your OpenAI API key, click Save, then Test. Pick a model under "Model": the list loads from your OpenAI account, and leaving it empty uses the default model. Then choose OpenAI as the engine in the new-book wizard, or for an existing book under "AI engine for this book" in the book's details. You need an OpenAI API key with credit on it (from platform.openai.com); a ChatGPT Plus subscription does not include API access. In earlier versions an OpenAI key was only used for AI covers. OpenAI is a paid engine: BookyAI never uses it unless you chose it for that book.