With search, there are actually 2 different products. The index itself is a textbook natural monopoly. There's no upside in having more than 1 web crawler as long as it can be trusted to just crawl the web but there's plenty of downside in the form of increased bandwidth costs for web sites. The actual search rankings are where competition makes sense. So spin the Google search index off as a non-profit that makes its product available at a reasonable cost to anybody who wants to run a search engine.
Then you spin off the rest of Google as separate companies. Android/Pixel, Google Ads/Analytics, Youtube, Chrome, Gmail/Docs/Drive and Maps/Cloud would all be separate businesses. Chrome would likely be best spunoff as a non-profit as well, operating an open source web browser project.
Of course, if you're going to break up Google you also have to break up the rest of FAANG too or they're just going to step right into the space vacated by Google and probably buy up the Baby Googles[0]. Apple would probably need to be broken up into a hardware company, a software company and a services company. Amazon would need to be broken up into AWS, Amazon Shopping and Prime Video. You could arguably even break Amazon Shopping up into the online store and the logistics company. Microsoft would need to be broken up into Windows, Office, Xbox, Bing and Azure. Xbox would then itself need to be broken up to unwind all of its purchases of independent video game companies. If you're breaking up Xbox, you also have to do the same with Playstation (spinning them loose from Sony and unwinding their own acquisitions). It might also be a great idea to then do the same with major 3rd party video game companies like EA, basically unwinding all of their acquisitions. Meta would need to be broken up into Facebook, Oculus, Instagram, WhatsApp and Meta Ads.
Once you start breaking up Google, you open up Pandora's box and basically have to keep going until you break up the entire tech sector. That's why it is so tricky to do it. Once you're done with tech, it'd be a good idea to look at other sectors such as health care, Hollywood and the news media where consolidation has been rampant over the past few decades.
[0]: https://en.wikipedia.org/wiki/Regional_Bell_Operating_Compan...