Not super wealthy. The most famous guy she adopted was some dude who was a simple bank clerk, before he opened a number of sauna clubs (aka brothels) in Germany. So he was as wealthy as the owner of a used car dealership. He actually bought the title for as little as €1000/month (until the death of the princess 3 years later).

He later married legendary actress Zsa Zsa Gabor, due to which he became very famous in Germany. Of course later he participated in various trashy reality TV shows and was always known as Frédéric Prinz von Anhalt and not by his real name Hans-Robert Lichtenberg.