Does 28 USC 3002 say the United States is a corporation?
Yes, but this is misleading.
(15)“United States” means—
(A)a Federal corporation;
(B)an agency, department, commission, board, or other entity of the United States; or
(C)an instrumentality of the United States.
This appears to say that the US is a corporation, but that’s not really what it means. This means that when you see the word “United States”, you should read it as one of those things above. But more importantly, at the very beginning of the section it says:
As used in this chapter:
Which means that this only applies to the chapter, not to all law or even the constitution itself. This chapter is chapter 176: Federal Debt Collection Procedure, of title 28: Judiciary and Judicial Procedure.
As an example, we can look at one of the laws that uses the term “United States” as defined above in sectino 3201:
3201 (f) Sale of Property Subject to Judgment Lien.—
(1)On proper application to a court, the court may order the United States to sell, in accordance with sections 2001 and 2002, any real property subject to a judgment lien in effect under this section.
You can substitute United States here with the definition above. In that context it makes sense to understand that a court can order a federal corporation, agency, or instrumentality to sell real property.
This distinction is important and most legal definitions only apply to a limited scope. Many sources that do not understand that will take them out of context and make claims based on this misunderstanding of the law.