“Lincoln believed in the Founders’ concept of a federal republic where the states were sovereign in their realm and the general government was sovereign in its realm.”
What Lincoln championed was the elimination of any substantive state sovereignty, and the subordination of the states to the federal government. The Founders’ intent was pretty much the polar opposite. I think the 14th Amendment, which is sometimes called “The Lincoln Amendment” (though drafted and passed after his death), addresses this, as before the passage of that amendment the Bill of Rights was only applicable to the federal government; the 14th Amendment made the BOR applicable to the states, as well. Like many things, there are pros and cons to this. The most obvious and drastic result of the 14th Amendment and its aplication was that the federal government became supreme, which was what Lincoln had always desired.
You clearly are of the Lincoln school, as evidenced by your comments. On the other hand, I am of the Jefferson/Madison school, which insisted on a limited and benign federal government whose authority was pretty much limited to acting as agent for the states, with a few exceptions. Again, arguments can be made for and against both schools. I think the Founders foretold this, as they created the Republic to function in such a way that in the event of a national emergency (such as an invasion by a foreign power) the federal government would ascend to dominant authority, but absent a national emergency the states should reign supreme.
In any event, I don’t think anyone envisioned the monstrous beast that the federal government has become.
No conservative likes that. I certainly think Lincoln would be appaled if he could see it. But without secession all that was likely to happen under his administration was Congess keeping slavery out of the territories and a moderate rise in constitutionally mandated tariffs. Hardly a rampant federal government. I do not think it's correct to assume that we wouldn't have an even more intrusive federal leviathan had Lincoln surrendered to secession.