Sorry, you are incorrect.
Private property rights deals with the right of the owner (be it an individual, corporation or state) having the right to determine the use of that property. This is in contrast to squatters rights which follows a collectivist view that the needs of the many are more important that the owner and thus, the group can take from the owner.
State’s rights deal with the enumeration of powers in the Constitution and those powers not enumerated being reserved to individual States.
Regulation of land owned by the federal government is one of the enumerated powers in Article 1 section 8 of the Constitution. So your assertion that such regulation is unconstitutional is demonstratively false.
You don’t give two twists about the Constitution.
That’s an awful broad interpretation of Article 1 section 8 give that it wasn’t purchased with consent of the legislature for the purposes of forts, etc...
Article V of the treaty of Guadalupe Hidalgo merely describes the new U.S.–Mexico border. The state of Nevada should by all rights have been encumbered with the vast majority of the states land either through cession to same from the government, or the allowance of general purchase to the state/public (which was done in small increments under 1872 mining law until the Clintoon moratorium on issuance of Patents).