“How did it come to pass that the Feds own most of Nevada?”
If I recall correctly, the United States took the land that became Nevada, plus a lot of other land, from Mexico at the end of the Mexican-American War. They paid Mexico afterwards, but they took it first. Then they established Territories on the newly acquired land.
The Second Paragraph of Section 3, Article IV of the US Constitution states in part: 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;
At the time, that was mostly the Northwest Territory, but later other Territories came to belong to the United States. (An interesting question is: By what Constitutional authority did those other Territories come to belong to the United States?)
In the case of many (not all) states beyond the first thirteen, said states were formed from the territories which were owned by the United States. Not the United States Federal Government, the United States.
Bearing that in mind, in many cases all of the territory/land/property within the bounds of a newly formed state was not granted to the State upon its Statehood. Some was retained by the United States.
We’d have to look at the Enabling Legislation for Nevada statehood to see the details regarding the original land granted or not granted to the State of Nevada.
Federal ownership of 87% of Nevada land was a condition of admittance into the Union.
Same with many western states. Of course, to you easterners, it's inconceivable. To us westerners, it's a source of friction, as eastern states were held to no such condition in order to gain statehood.