From https://www.chromium.org/developers/how-tos/api-keys:

> Some features of Chromium use Google APIs, and to access those APIs, either an API Key or a set of OAuth 2.0 tokens is required. Setting up API keys is optional. If you don't do it, the specific APIs using Google services won't work in your custom build, but all other features will run normally.

From experience, running without API key means that the browser will nag you at every start. If it doesn't, you do have them and then the browser uses APIs mentioned on the page.

This was one of the more egregious ones from a few years ago; since fixed, but as far as I'm concerned the trust was permanently broken (what's to stop them from doing something similar and hiding it better, after all this made it past the package maintainer until a user complained).

https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=786909