Fortunately I found a work around. Google Reverse Image search allows me to nail down the style fairly accurately. For example, I was able to find the style of one image to accurately duplicate the style as "Futuristic Art Deco Design with Cubism, Neo-Classicism, and the work of Italian Mannerists" in just a couple of minutes.
Otherwise its just inconvenient. Its easier to share without the prompt.
Also prompting is trickier with model like SDXL that have seperate content and style prompting. Users often dont even know the full prompt.