I'm not so sure about that. They have kind of opposite incentives to OpenAI. OpenAI starting without much money had to hype the AGI next year stuff to get billions given to them. Google on the other hand is in such a dominant position with most of the search market, much of the ad market, ownership of Deepmind, huge amounts of data and money and so on probably don't want to be seen as a potential monopoly to be broken up.
Also Sergey Brin is back in there working on AI.