sophisticated is standard American English, and suitable for formal contexts. It can have a range of (related) connotations depending on context.
In a technical setting, you might describe an algorithm, machine, proof, or logical argument as "sophisticated". This carries connotations of complexity, refinement, and being highly-developed.
Any of the following would be valid.
"Naively, we would expect
foo, but a more sophisticated analysis suggests that
"Mammals display sophisticated social behavior."
"By using a sophisticated language model, we increase our speech-recognition accuracy by 17%."
In non-technical contexts (like your example of a socialite), there are also connotations of being worldly or cosmopolitan.
English gets this word directly from Latin (via Greek), based on the familiar "soph" root (meaning "wisdom").
I know only a couple dozen words of German, so I can't claim authority, but two minutes on Google turns up other non-cognate German words with the same meaning. If I had to bet, I'd guess that the borrowing went from English-->German rather than the reverse. (Of course, German could have appropriated the Latin in parallel, but I think Latin roots are pretty rare in German. (Someone correct me if I'm wrong on that.))