Probably so that they may track which searches people are performing on DuckDuckGo

sad but true. I'd be interested to know if this data (i.e. non-Google search engine queries) is sent to Google. I'm assuming it is.

Is there a Chrome extension that shows to the user what information exactly Chrome is sending home?

Give Google some privacy of what is being sent home :)

Chrome (and Chromium) creates at start and maintains SSL connections to Google. It is not easy to sniff what is being sent. Even if you MITM it, like in enterprise transparent proxies, Chrome will throw an error because of cert pinning. google domains should be whitelisted: "we recommend that you avoid the use of transparent proxies." https://support.google.com/chrome/a/answer/3504942?hl=en

Seems like patching that out of binary would be trivial task.

But I doubt the Chrome extension that would do that patching could stay at Chrome store.