Title to all lands outside the original 13 colonies was originally vested in the federal government.
“and to exercise like authority over all places purchased by the consent of the legislature of the state in which the same shall be, for the erection of forts, magazines, arsenals, dock-yards, and other needful buildings”
You see, in these states the federal government didn’t purchase the land, with the consent of the state legislature, for the very simple reason that the state didn’t exist. The federal government owned all the land in the territory except insofar as it sold it to private parties.
I’m not familiar with every state, but in MO, not generally considered a western state, the federal government was still selling rather large amount of public domain land off in the early decades of the 20th, and some as late as the 50s and 60s.
There seems to be a common belief that western states were screwed by the feds in some ways, that states farther east had the public lands deeded to them at statehood. AFAIK, midwestern states were dealt with more or less as western states were. I’m willing to be convinced otherwise, if anybody has, you know, evidence to that effect.
That large amounts of western land are still owned by the feds is primarily, though not exclusively, due to the fact that for about a century nobody wanted to buy the land. It wasn’t worth anything to anybody. With exception of lands with large mineral deposits, most of it still isn’t.
I have personally walked large distances on these lands in CO, NM, UT, AZ and WY. There is a really good reason nobody has bought it. The land has no value.