Kind of and kind of not. Their main resource of serving ads is getting legitimately eaten away. The route to getting AI to replace those ad dollars isn't clear and the capex to build it out is significant. Google has to manage a variety of assets that are currently lucrative but under threat. Yes they don’t have all their chips in one basket but it isn't clear that helps them in the race… it hasn’t so far.

Moreover, Google is getting paid out by both to serve their models.

their stable income is eaten away by the quickly rising income of the labs, they will be out of the race once the labs reach a certain threshold of income, rather sooner than later. Unless many people install Google surveillance anti-gravity thing on their system which I doubt