If you want to understand Civil War tactics it is best to study Baron Jomini’s The Art of War, as study that many Civil War officers were familiar. Sun Tzu was unknown to the West during this time period and its Oriental mysticism would have been unpopular.
This may surprise many but Sun Tzu is NOT given much credence in higher professional military circles. Sun Tzu is considered too much of military fantasy and a work that ignores human nature to be of much use. See Michael I. Handel’s Masters of War: Classical Strategic Thought for more commentary on this subject. Clausewitz is given much greater authority today. Both Sun Tzu are too formulaic and didactic while Clausewitz is dialectic.
If you want to understand Civil War tactics I recommend the following works
Brent Nosworthy’s The Bloody Crucible of Courage: Fighting Methods and Combat Experience of the Civil War
Paddy Griffith’s Battle Tactics of the Civil War
Earl Hess’s Civil War Infantry Tactics: Training, Combat, and Small-Unit Effectiveness and
Civil War Logistics: A Study of Military Transportation
The latter is a pre-order, but it will be an excellent work. I have seen the manuscript.
For the record, I am a retired US Army Lt. Col., and graduate and lecturer at the US Army War College, at Carlisle.