If Google wanted - they could've easily released ChatGPT version that is 100x better than current one considering they invented the technology and they have thousands times more and better data to train it.
They just weren't interested.
The impressive thing with chatGPT to me is how well it understand what you want even with very sparse input. Even if it gives wrong answers it still feels like you are both on the same page. That seems like the secret sauce even if a larger language model would give more correct output. I wouldn't be shocked at all if Google doesn't have anything currently that feels the way chatGPT does when it comes to interaction and now they are racing to build exactly that.
I wouldn't be surprised if they used anonymized gmail data though. Even if they removed all proper nouns it'd probably provide a lot of extra tokens for training.