I don't think Google uses data from Chrome this way. I don't think Google actually wants to associate data with people so aggressively. It's obvious when that happens and it feels gross (this is why I stopped using Facebook 10+ years ago, I've never had an equivalent gross-out moment with Google).

I'm guessing the reason google doesn't use third party cookies is because they get higher quality data from people being signed in to Google services, and that is independent of whether they are using Chrome or not.

No, the antitrust argument is Google doesn't need third party tracking because they have a huge amount of first party data and ad inventory from search and YouTube and all their other web products. It's not from Chrome. Their adtech competitors don't have first party inventory or data and would be crushed.