。
She's rich, but she isn't happy.
Literal
She [topic-は] rich [despite-なのに] happy is-not.
なのに is the noun/な-adjective version of the concessive のに — 'despite being X.' The な before のに is needed because 金持ち is a noun: 金持ちなのに ('despite being rich'). For verbs and i-adjectives, plain のに attaches directly: 行ったのに ('despite going'), 高いのに ('despite being expensive'). のに carries an undertone of unfulfilled expectation or mild frustration — 'and yet.' The wealth-without-happiness pairing is one of the most universal narrative tropes, and のに fits its emotional shape exactly.