I left the Gemini model on Automatic. Does it start over with the same model every time I open BookyAI?

Not any more. On Automatic, BookyAI rotates between Gemini models to make the free limits go further. From version 1.9.21 it remembers the model it settled on and carries on with it after you close and reopen the app, instead of starting the rotation over every time. The Model list in Settings shows it: "Automatic (rotation), now" followed by the model in use. If you prefer one particular model, pick it in that list.