Not really: the stipulations in the agreement you make with the cloud provider explicitly cover data rights. Rights to subpoena data is completely different.

You are right about the implications, but this is old news. This is what is known as the "third-party doctrine" and it goes back decades. It is not an entirely unreasonable doctrine, based on the history and text of the 4th amendment. More importantly, Judge Pauley is obligated to follow Supreme Court precedent on this issue. Our system of law is based heavily on "stare decisis", or the idea that we should follow precedent and not keep re-interpreting the law or changing the settled expectations of society.

That said, at least some members of the Supreme Court have expressed concern about how much the 3rd party doctrine guts our privacy rights in the modern age. In a recent case (Jones), the Supreme Court held that attaching a GPS receiver to a car violated the defendant's rights because there was a warrantless intrusion when the device was physically placed on his car. For now, they side-stepped the issue of what would happen if, for example, the police collected all of your movements from a 3rd party like OnStar, which uses your car's built-in GPS. Judge Sotomayer, in a concurring opinion, discussed how the 3rd party doctrine may have to be changed:

"More fundamentally, it may be necessary to reconsider the premise that an individual has no reasonable expectation of privacy in information voluntarily disclosed to third parties. E.g., Smith, 442 U. S., at 742; United States v. Miller, 425 U. S. 435, 443 (1976). This approach is ill suited to the digital age, in which people reveal a great deal of information about themselves to third parties in the course of carrying out mundane tasks. People disclose the phone numbers that they dial or text to their cellular providers; the URLs that they visit and the e-mail addresses with which they correspond to their Internet service providers; and the books, groceries, and medications they purchase to online retailers. Perhaps, as JUSTICE ALITO notes, some people may find the “tradeoff” of privacy for convenience “worthwhile,” or come to accept this “diminution of privacy” as “inevitable,” post, at 10, and perhaps not. I for one doubt that people would accept without complaint the warrantless disclosure to the Government of a list of every Web site they had visited in the last week, or month, or year. But whatever the societal expectations, they can attain constitutionally protected status only if our Fourth Amendment jurisprudence ceases to treat secrecy as a prerequisite for privacy. I would not assume that all information voluntarily disclosed to some member of the public for a limited purpose is, for that reason alone, disentitled to Fourth Amendment protection. See Smith, 442 U. S., at 749 (Marshall, J., dissenting) (“Privacy is not a discrete commodity, possessed absolutely or not at all. Those who disclose certain facts to a bank or phone company for a limited business purpose need not assume that this information will be released to other persons for other purposes”); see also Katz, 389 U. S., at 351–352 (“[W]hat [a person] seeks to preserve as private, even in an area accessible to the public, may be constitutionally protected”). Resolution of these difficult questions in this case is unnecessary, however, because the Government’s physical intrusion on Jones’ Jeep supplies a narrower basis for decision. I therefore join the majority’s opinion."

Thank you for educating me with that extremely relevant quote!

Even further: We don't possess the copyright to the algoritms of non-plaintext. So effectively we don't own anything we codify in a proprietary format...

Which is why Richard Stallman was right all along.

I'm with the other poster who intimates that something extremely egregiously bad just happened out of this.

It's just not about the government's structuring anymore. A term in the Fourth Amendment just got emptied of all semantic value ("effects").

They just globally refactored the entire legal system.