Once an Ordinance of Secession is passed, all “public” property became the property of the State, ie, South Carolina. It was as if South Carolina had never been a part of the Union. An “anullment” if you will.
South Carolina had no jurisdiction over Federal forts, built on land they had ceded to the Federal government in toto. They could no more claim Sumter than they could claim Washington DC or Kansas or the land under any random building in Charleston. It was owned, not by "the public", but by the Federal Government under Article I. It was paid for by the taxes of ALL the States, and the willingness of SC and the rest of the South to simply steal the joint assets of the United States is a prime example of why unilateral secession is unlawful.
If your legal theory of ownership were to hold, then it would negate land ownership; the State could just declare any land theirs and take it at cannonpoint, maybe to pay later, maybe not. Now, maybe the goal of South Carolina was to set themselves up as a "banana republic" complete with "nationalization" of whatever they wanted, but they at least claimed to be a democratic republic. Their deeds belie that.