Maybe I am misunderstanding, but I just tried that flow with a Pages document and it still works in Sonoma. Drag the icon from the header, drop into an email. Now I'm curious what the old feature was.
What's changed is that newer versions of the OS hide the file proxy icon by default. You have to hover the cursor over the title for a second to see it, or to interact with it. Before, it was always visible, and ready to be clicked + dragged.