I'm unaware that land within a state that is not privately held is presumptively the feds for the taking or controlling. Your quote from the Constitution (need a cite) addresses "territories" or federal lands. How is land within a state "territory"? And if something is federal land, there should be a constitutional reason for its ownership because, as the Tenth Amendment confirms, the federal government needs a constitutional reason for anything it does because the Constitution is it's only source of authority.
STATES RECLAIM THE LAND the feds unconstitutionally possess. Would be interested where you find this in the Constitution.
States and individuals need no Constitutional authority to do something if not expressly forbidden in the Constitution, again, as confirmed by the Tenth Amendment. Unless the feds have constitutional grounds for their acts, the states and people may nullify and reverse unconstitutional federal acts.
Territory here refers to land in the possession of the United States, not "territories," the administrative divisions later set up by Congress on its Territory.
The state of OH was admitted in 1804, I believe. The vast majority of its land was at the time public domain land. Congress did not turn over that land to the new state. It allocated 5% of the proceeds of the sale of that land by the United States to individuals to Ohio, but required the state to spend the money on roads.
When other states were admitted, they generally followed this precedent, without exception I've seen. Land that hadn't been sold by the feds prior to statehood remained as property of the federal government until it was sold.
The problem is that in much of the West, primarily for location and water reasons, nobody bought the land.
Some of it was withdrawn from potential sale starting in the late 1800s to form what eventually became the National Forest System. Most of the rest was eventually administered by the BLM, but was largely still available for sale till the 50s or 70s.
The Constitution gives complete power over property owned by the United States to Congress, which can pass a law to grant it to state ownership. Or not, as it chooses.
But there simply is no constitutional issue here.
Whether Congress uses its power wisely is of course a separate question entirely.