You are correct, that section assumes the state is already a state, otherwise the land could not have been bought from it by the feds in the first place.
The question then is, what does the Constitution say concerning how States get created and added?
Did it have provisions for territories being created first, and then States?
And how is it that the Midwest States, from Oklahoma up to the Dakotas, have less percentage of federally owned land than the States to the west of them?
(Texas was its own nation, thus the tiny percentage of fed owned land there)
That would be Article IV, Section 3.
Did it have provisions for territories being created first, and then States?
Yes. "The Congress shall have power to dispose of and make all needful rules and regulations respecting the territory or other property belonging to the United States; and nothing in this Constitution shall be so construed as to prejudice any claims of the United States, or of any particular state."
And how is it that the Midwest States, from Oklahoma up to the Dakotas, have less percentage of federally owned land than the States to the west of them?
To answer that I would suggest you read up on the Northwest Ordinance, Louisiana Purchase, the Mexican American War, the Gadsden Purchase and the purchase of Alaska.
I believe the federally controlled land was a condition of statehood for most western states. It seemed not to have occurred to the Feds, or was deemed inappropriate, prior to around 1850.
As an aside, the admission of states is another example of Congress authorizing the President to negotiate agreements in behalf of Congress.