Ukraine has not taken the city of Kursk; they have merely taken some, mostly rural, parts of the oblast, or region of Kursk. The largest town they have taken as of this writing is Sudzha, which has just over 6,000 people.
The Russo-Ukrainian War was far different from the American Civil War, and Ukraine was, of course, not anything morally resembling the Confederate States of America.
It's pretty funny how they go out of their way to avoid making the obvious comparison with the first nazi invasion of Kursk, because all the same points could've been made with it too.