The "proprietary changes that google adds" are API keys[1], branding, and external plugins like Flash/Widevine. Other than those, the source code is identical.

[1]: https://www.chromium.org/developers/how-tos/api-keys

> Other than those, the source code is identical.

How do you know, and how can we prove it?

You could decompile, inspect, and debug chrome if you must, but doing something so easily viewable and auditable would be a huge blow to their reputation.

TIL. Are there any downsides to running Chromium instead of Chrome?

Chromium has no auto-updater on Windows and macOS. Unless you have a package manager that compiles updated versions for you, you're better off using Chrome.

I use Firefox. But, I'd be willing to install a version of Chrome if it came without all of the Google garbage pre-installed. I was hoping that maybe Chromium could fill this role.

There's a project that does exactly this. (I can't comment on the quality or the trustworthiness.)

https://github.com/Eloston/ungoogled-chromium

I have used it in the past but now I use Chromium instead as a Chrome replacement since it is more stable than ungoogled-chromium.

I use Firefox as my primary browser and Chromium for testing things for Chrome. The only downside to Chromium is you have to update it manually by downloading the package and dragging it to your applications if you use Mac. Other than that, it works perfectly. I trust Chromium more than Chrome if I want to let it run in the background.