It is being litigated.
> Five justices — the three more liberal justices, plus Chief Justice John Roberts and Associate Justice Brett Kavanaugh — supported keeping the moratorium in place. However, Kavanaugh emphasized in his appended statement that he agreed to continuing the moratorium only because it was about to end. As a matter of law, Kavanaugh wrote, he thought extending the moratorium further was unconstitutional.
https://www.nbcnews.com/politics/white-house/trump-gives-cdc...
> Biden said on Tuesday he had sought out constitutional scholars to determine the CDC’s legal authority and “what could they do that is most likely to pass muster constitutionally.” The “bulk” of the scholarship reviewed by the White House said additional action by the CDC would not pass muster in the courts, Biden said, adding that there were some “key scholars” who said it could.
https://www.politico.com/news/2021/08/03/eviction-moratorium...
The bulk of constitutional "experts" said it wasn't constitutional. He found one or more that didn't agree with that assessment, so he went with the few against the majority.
https://www.supremecourt.gov/opinions/20pdf/20a169_4f15.pdf
The actual text of the ruling is simply: "The application to vacate stay presented to THE CHIEF JUSTICE and by him referred to the Court is denied." The additional wording that follows is simply Kavanaugh's personal feeling on the matter which for now doesn't carry the force of law, as well as several judges lamenting they would've vacated the moratorium if they had the votes, which they didn't.
(Note: I happened to agree that Biden should not have extended the moratorium. And it may yet prove to be that he will be overruled by the US Sup. Ct., but that hasn't happened yet.)
Of course, the very low rates, high construction costs, demand to leave cities, and various other factors also come into play. However, yesterday I was very surprised to learn that the eviction moratorium that is preventing landlords from selling their properties is actually an order from the Centers for Disease Control. When and why did that organization get that sort of power?