“why do chasidim dress in the same clothes as 19th century Russian nobles”
They don’t. Where did you get such an idea? In fact, the “levush” was so distinctly Jewish it was banned in the Russian Empire in an effort to modernize and assimilate Jews. That is why Litvish and Lubavitch where western style clothes because of the gezeiros forbiddin the Jewish levush. Before those gezeiros basically all European Jews more or less wore what you are calling the way “chasidim dress.”