It’s not your personal data. It’s Google’s log of requests made to and carried out by Google’s servers. It’s not covered by the literal text of the fourth amendment—which, as you correctly paraphrased, applies to one’s own person and property. The fourth amendment was also never understood at the time it was written to apply to third party business records, which is what your search history is. (While we didn’t have search engines in 1789, we had all sorts of commercial businesses, from banks to accountants to merchants, who kept sensitive customer records. Indeed, for at least 400 years, such records have been obtainable in civil suits with just a subpoena.)

I think it would be a good idea to require a warrant in such cases. But it’s not a 4th amendment issue.