From my experiences with Google integrated AI, I'm skeptical that Google can win any battle with it.
ChatGPT and other modern AI tools are useful specifically because they do what I want when I want to do it. Compare this to Gmail's smart compose: by the time the AI makes a suggestion I'm already half-way through typing that text, so its prediction is completely useless even if it's correct.
(Also, I really enjoy the random historical rambling at the end of some Stratechery articles).