You don't understand how lucrative search is by itself. Google pays to monopolize search because they make a lot of money from the paid promoted search results (AdWords). Those can be personalized but most of the time they're simply based on your query.

The personalization profile based on searches and other stuff is used for their display network (ads across the web), but that entire network is way less valuable than Google Search alone. [0]

[0] https://abc.xyz/investor/

That would solve only a tiny part of the problem. The elephant is the monopoly on search. Ironically, most probably MS is beating them around this time with more powerful search tech and it will be time to anti-trust MS.