Ultimate General: Civil War.... it has a few oddities they need to work on, but it is hands down the best American Civil War game I have ever played.
I will warn, you have to do a fair bit of micro-management outside of battles, but it is built in a way where the learning curve is almost nonexistent and getting to customize your Corps, Division, Brigades is fun.... you can choose their weapons, officer in command, and you decide how to replenish units after battles.... pay for veteran replenishment or live with rookie replenishment? Should your skirmisher unit be carbine-carrying, short-range? Or should they be sharpshooters with long range weapons?
After a battle your forces will have of recovered casualty weapons and also captured some enemy weapons which go into your armory and you can buy/sell from/to your armory.
If you like RTS battles with a mix of micro-management outside of battles, this game does all of that quite well.