Did you note that the OP said it is a well known psychological phenomenon and not some utopian enlightened state that most of us can only aspire to attain?

And fwiw, Schopenhauer knew about Buddhism very well and talks about it in length in his essays on pessimism. What he means by attachment here is in fact, the Buddhist equivalent of craving. What you own can add to your vanity, but it is what you do not have or are longing for(in this case more money) that shows your true inclination, which Schopenhauer describes as worth. It does not mean that money has no worth, it means that the money that you already own has way less worth than what you don't. Aphorisms are pithy for a precise reason ¯\_(ツ)_/¯