The obvious place to start splitting is to separate search from other things, like a non-search ad business, an OS, a browser, a mail client, a mapping and navigation business, and hey, another OS.

But I don't think it's impossible to split up search, either. I'm sure that Google doesn't just have 1000s of people working together in one big room with no structure. Their current organizational lines could tell us a lot about useful ways to break it up. Historically, for example, there were search infrastructure providers like Inktomi that sold services to consumer-facing search engines. Maybe a crawling-and-archiving group is separable; there are times I sure would have paid Google to use their crawl rather than doing my own. Parts of search were previously separate companies that perhaps could be spun out again. E.g., a lot of the structured-data stuff was once Metaweb.

You silo the search engine segment of the business as one company, the advertising segment as a separate business, etc etc. Alphabet is more than just the Google search engine at this point.

You would probably split google's search engine off from the rest of their services/products, so that they can't use their search engine dominance to unfairly harm competition.

Similarly, you could divide Amazon into a platform company that does fulfillment for others and a separate company that sells their own products, as well as splitting off things like AWS into their own companies.

Maybe that's not the right line to split across.

Keep search intact but mandate that it must offer equal access to 3rd parties to match any access it has internally.

(How you do this without a privacy disaster I'm not so sure about)

I'm thinking along the lines of privately held public infrastructure like local loop unbundling in telecoms.