I'm not as criminal lawyer but are these properly considered warrants or even a search and seizure of the suspect? This is more like a subpoena against a third

I'm not as criminal lawyer but are these properly considered warrants or even a search and seizure of the suspect? This is more like a subpoena against a third party not the suspect.Even if the data is considered the suspect's, does a person have reasonable expectation of privacy when he knowingly and voluntarily uses search engines that are built specifically to profile users so that data can be sold or used for ads ?If he was using a VPN may be different story but particularly Google users should by now have no reasonable explanation of privacy.