Good to hear it.
Well, for most of the things, we would need to know the general direction the TL goes in. For example, if the CSA and the USA become friendly, and a NATO-type alliance is created, I see no reason that it wouldn't join. It would almost certainly join a United Nations-type organization.
In the most plausible scenario, to me at least, I see the CSA becoming a fairly powerful nation down the road, but not attaining the USA's level of power. I could see a Confederate navy with a modern fleet, with perhaps even a carrier or two. Technology, I suspect, would be roughly on the same page with OTL, give or take five years or so.
Conditions around the world, like I said, are hard to know without knowing the general direction of your TL. For example, the Middle East situation might be completely different, if say, the USA and Germany sided together against the CSA, France, and Britain and won World War 1.
So, I would probably see the modern CSA as the USA's kid brother, and while not being as powerful as the USA, it could very well be at the very least, a second-rate world power.