They probably remain prominent officers in the United States army, as many were before Secession. Some could maybe go on into politics; Robert E Lee in particular was highly praised in the US army before defecting, and his great personal charisma could lead to politics quite easily; especially as Zachary Taylor had already set a precedent of generals going into politics. I think President Lee is unlikely but possible. Though it's also possible that many of them would never have become so prominent without the war (certainly not so quickly). Lee, for example, was "just" a colonel at the start of the war, as was Jackson; Forrest was a businessman.
Of the not-so-famous but high ranking CSA officers, many had been high ranking in the US, too; for example, Samuel Cooper had been Adjutant General. Albert Johnston was commander of the Department of the Pacific. Beauregard was superintendent of West Point. Etc.
Most of those that had been private citizens wealthy enough to raise battalions or regiments, and then went on to be great commanders would probably remain in the private sector. Maybe some would be very successful, maybe some would be mediocre or fail, as the overlap between "great general" and "great CEO" is not universal.
But we probably wouldn't know almost any of their names.