It’s no secret that Google has a very large influence. They have influenced web pages into being highly optimized for high search engine rankings, and have pushed AMP: https://www.eff.org/deeplinks/2020/07/googles-amp-canonical-web-and-importance-web-standards-0. However I haven’t found any concrete examples of Google pushing web standards that have been adopted and require browser support. I’ve read comments here and there like this one, that the Shadow DOM was created and pushed by Google, perhaps to make it harder to block ads, but didn’t find any sources on that.
They really tried with Web Environment Integrity:
https://github.com/explainers-by-googlers/Web-Environment-Integrity/issues/28
There was enough pushback that they dropped that proposal, but expect to see it back in mutated form soon.