> we're talking Chromium, the underlying browser engine. As it stands, Chromium is the basis for a variety of browsers, not just Google's flagship. From what I can tell (as a non-expert on Chromium's source, so please correct me), the Googley stuff that makes privacy advocates nervous is independent from the core Chromium browser engine
This might be just me being pedantic, but I thought it might be worth mentioning...
Chromium is basically the same thing as Chrome, except that it's missing a few proprietary blobs that Google is not legally allowed to put into Chromium: some DRM stuff, a licensed H.264 codec, a Flash plugin, etc. But if you're worried about privacy, Chromium still has all the Googley stuff. You can still log into Chromium with your Google account, and it'll sync your bookmarks and history and passwords just like Chrome. Chrome extensions are 100% compatible with Chromium, and you can install them into Chromium via the Chrome Web Store.
Some people might be familiar with "Blink", which is the browser engine (and is a fork of WebKit). There's also V8, which is the JavaScript VM. These two components aren't enough to form a usable browser though. So the Chromium Project develops what is called the "Content module" (see https://www.chromium.org/developers/content-module) which combines Blink and V8, and some other pieces, to form a basic web browser. This is what other browsers (like Opera, and I presume Edge as well) are built on top of, and does not contain all the Google integrations that Chrome/Chromium have.
While Content is missing a lot of the Chrome features that make privacy advocates nervous, it's still a problem because most Chromium/Content developers are Googlers, and will probably not implement things like WebKit's ITP or canvas fingerprinting prevention.