No, the Grayzone claim is demonstratably false. They write:
Just days after the publication of Zenz’s paper, Pompeo issued a statement denouncing China’s alleged policy of “forced sterilization, forced abortion, and coercive family planning,” personally crediting “Adrian Zenz’s shocking revelations.”
This is apparently the entire basis of their claim that "the US government’s accusation of genocide against China stems from a single source" (you can check their article for yourself).
But nowhere has Pompeo drawn any connection between Zenz's paper and his determination that genocide is occurring. He does not say anywhere in his statement about Zenz's paper that he believes this is part of a case for genocide.
In the actual the text of his determination that genocide is occurring, Zenz is not cited. In fact, no source is cited! The tone of the statement is that of a conclusion being reached, not a full investigation.
The State Department already did an investigation into Xinjiang back in 2019. Among their sources, they cited National Public Radio, The Diplomat, The New York Times, the CBC, Radio Free Asia, Human Rights Watch, the BBC, and official CCP government websites that were archived by Zenz. At the time this had no policy consequences. [edited: my hypothesis for why Pompeo did not react in 2019 is removed as it is off-topic for this SE]
In any case, Pompeo is clearly relying on more than just Zenz even though his statement provides no citations. You can see this from the quotations he uses:
Meanwhile, they are delivering far darker messages to their own people, portraying Uyghurs as “malignant tumors,” comparing their faith to a “communicable plague,” and exhorting the Party faithful to implement a crushing blow, telling them “you can’t uproot all the weeds hidden among the crops in the field one-by-one; you need to spray chemicals to kill them all.”
These quotations are not attributed, but they do have origins. For example, the last and longest is from an RFA article, quoting a Chinese official overheard by the chief of security for Kashgar’s Chasa township, whose name is given as Yasinahun. If China wished to deny these statements they could simply produce Yasinahun or deny his existence.
The State Department relied on dozens of sources for their own understanding of Xinjiang, and even Pompeo relied on more than just Zenz. The Grayzone claim is therefore proven false.