Draggable icon in the title bar?

Solution 1:

In Big Sur, you can make the proxy icon appear immediately on title hover:

defaults write -g NSToolbarTitleViewRolloverDelay -float 0

In macOS Monterey beta 3, you can make the icon always show:
System Preferences → Accessibility → Display → Display (tab) → Show window title icons

Enable this from the command line by setting

defaults write -g com.apple.universalaccess showWindowTitlebarIcons -bool YES

Solution 2:

The draggable icon in the title bar is not gone in Big Sur, just hidden.

To display it, simply place the mouse over the document name for a second, and it will appear. Hold shift to remove the delay before the icon appears.

When the icon is visible, you can drag it to another folder as you desire.

Note that it is not necessary that the icon be visible if you just want to display the full path to the file. Either right-click the document title, or click the title while pressing the command key and it will appear instantly: