Apparently Google provided police with IP addresses, but not names [1]. Assuming that Google did not provide any other account details, the usage of a VPN service or Tor might be able to protect users in similar cases.
Or just use a sensible search engine like Kagi, which doesn't associate search queries with users (it doesn't need to; it's not in the business of selling users to ad brokers).
It's weird how easily we've acclimatized to creepy tech-company spying. For Google to snoop on your searches, record them, and permanently archive them for retrieval years in the future was a very creepy and ignominious business model, and it's embarrassing how readily we all went along with it, for the convenience.
iCloud Private Relay is double blind, so even if they did, they can't match it to the egress address. User -> Apple -> (Cloudflare, Akamai, others) -> Public.
https://help.kagi.com/kagi/faq/faq.html#why-trust
It's weird how easily we've acclimatized to creepy tech-company spying. For Google to snoop on your searches, record them, and permanently archive them for retrieval years in the future was a very creepy and ignominious business model, and it's embarrassing how readily we all went along with it, for the convenience.