Edge is the number one browser in the world for installing chrome.
Doesn't Chrome send your entire browsing history to Google as well? Edit: I thought this was a well know fact and if it isn't I might have been to harsh about Google and Chrome. Edit 2: Thinking about it and searching a bit I conclude that IIRC Google at least used to have access to your browsing history as part of syncing it unencrypted.
My sync is encrypted so I can't test this for you but I believe if it's not, you can check (and clear) your history here: https://myactivity.google.com/myactivity
Google's privacy policy seems to make it clear that this happens unless encryption is turned on: https://www.google.com/chrome/privacy/index.html#signed-in