Sure Google is a lot more than search at this point, so it's not the right mission. Though, I would say "organizing the world's information" is at least one of the right missions for the company.
Funny enough - Satya Nadella introduced a new mission statement at Microsoft shortly after he became CEO[1].
It's pretty anodyne, but by design - it's a way to push the company towards different ways of operating by creating a pretext to say "X project is part of the new mission and here's why" from a top-down perspective.
It sounds pretty generic for me. I mean, Google sells productivity tools and services. "Improving productivity" is just table stakes, not something that's a useful mission statement. Vague or overly broad mission statements are pretty much the same as no mission statement at all.
Larry Page said almost 10 years ago (!!!) that Google's mission probably needed to be updated. That's a long time to be lost in the wilderness.
https://www.theguardian.com/technology/2014/nov/03/larry-pag...