I think you are confused about the Vicksburg campaign. Grant had superior numbers throughout relative to Pemberton, and even, though not by much, against the separate forces of Johnston and Pemberton, who of course were never able to combine forces against him.
Per southern regiments in the Union army. SC was the only state that didn’t produce at least one such (white) regiment.
When conducting a river crossing there is a time when small forces have crossed, and others have not. So it was at Vicksburg, when Grant had crossed at Bruinsburg with small forces, Pemberton did nothing. Grant’s larger forces west of the river could do nothing. Eventually more of Grant’s forces got across, and yes, then he had superior forces.
You are right, I did make the error using Pendleton instead of Pemberton. Pendleton was a confederate artillery officer, but not the Pennsylvanian in command of the defenses of Vicksburg.