There's not anyone rooting for Google to win; it's lost a whole lot of cred from technical users, and with the layoffs and budget cuts (and lowered hiring standards) it doesn't even have the "we're all geniuses changing the world at the best place to work ever" cred. OpenAI still has some mystique about it and seems to be pushing the envelope; Google's releases seem to be reactive, even though Google's actual technical prowess here is probably comparable.