It is so interesting to me that you asked about this. I caught myself using this phrase a few weeks ago, and I thought I might ask others if they would still use it.
In my use, I meant it in its extended vernacular sense: someone who behaves in an excessively self-centered way, self-indulgent, demanding, prone to tantrums over small matters, appropriating goods and services heedless of the inconvenience or impact on others. Essentially, behaving like a spoiled child.
I would have little occasion to use it in its original formal sense as the principle female singer, since I'm not an opera-goer.
I did, in fact, use it in reference to a man, despite its clear reference to a woman in the Italian. That was to be my question. Would others consider using this phrase in its informal sense in reference to a man?