You cannot inspect the exact status of enemy stacks, but you can inspect your own, and realize the enemy operates exactly the same as your forces.
If you select a stack, in the lower righthand corner the inspection panel for the stack opens. Here you find, directly underneath the -activation envelope- the GS (General Supply) icon, which looks like a tent with a crate inside. The tool-tip of this icon tells you what percentage of its supply capacity your stack is carrying, how many GS supply points that is, and how many GS that stack uses each turn.
Looking at a corps stack with 2 full divisions and 2 supply train units I see they are at 100% supply capacity, they are carrying 294 supply points, and use 74 GS per turn. So this stack could operate away from every supply source for 4 turns, before it starts taking hits and losing cohesion through a lack of supplies.
From your description of the Battle of Springfield, the Confederate stack is about 2 divisions, with (2 supply trains? "It did have 2 4 unit wagon trains". Do you mean 2x 4 element supply trains? I'm guessing so.), so they should have about 4 turns before it starts to hurt.
Are you certain Athena didn't build a depot in Fayetteville? Fayetteville is 2 regions distant from Springfield, so a stack marching from Fayetteville should be able to be reached Springfield easily in one turn in fair weather.
There were a number of battles in Springfield. I know you can capture WS (War Supplies) through destroying elements in battle. I believe you can also capture GS, but I'm not 100% certain.
I don't think the South can take any supplies from the depot in Springfield (should be there per default, I believe) as long as at least the garrison is in the city, but if there is a depot in Fayetteville, the CS stack could be pulling some supplies from Fayetteville, albeit not huge amounts, but possibly enough to prolong their field operations.
You are playing on AI Level: Colonel. Above Lieutenant, Athena does not get 'better', but she is given many advantages, such as all her leaders have all their standard values increased by +1. I believe cohesion loss through movement is also reduced. This is why I never play on levels above Lieutenant. I don't want to get used to playing an opponent I could not confront in PBEM, which, as great as Athena is, will still always give a more exciting and interesting game. Human opponents can be very unpredictable.
Although you didn't mention it, I imagine in your game you have given Athena a higher detection bonus. This allows Athena to target areas further that you would expect her to be able to 'see', which leads to her mounting far reaching excursions into your hinterland. If you don't want Athena to be ranging out to those weakly protected major cities, don't raise her detection bonus above 'low bonus', one step to the right.
So, in general, if you don't want Athena to act like an Übermensch, don't equip here with superhuman characteristics.