Google Play Services (on Android) is not a search engine or a browser, either.
Google Home does not serve ads, either.
My original comment's grand-parent did not claim if Electron was a browser or a search-engine, or if it showed ads, just that it is not necessarily independent of Google services just because it's built from Chromium.
For a benign example: using Google search
For a less benign example: your browser/device/network being tracked for ads when using Google search