Not to fully excuse Google's behavior, but baking that behavior into an operating system seems far worse than putting nags on a website.

Google's prompts weren't that different than those "Get Firefox!" badges people used to put up in the 2000s.

It's not illegal to promote something. What's illegal is overtaking a new market by pushing your stuff via already established monopolies in entirely different markets (at least under EU-law). Which is why Microsoft is taking action (and google stopped pushing their browser via their search engine)