Drag and drop is now supported on Windows 11 build 22557 or later. Reference can be found in official post of 22557, under Changes and improvements > Taskbar.
Drag and drop is now supported on the Windows 11 taskbar. Quickly drag and drop files between app windows, by hovering over apps in the taskbar to bring their windows to the foreground. Try attaching a file to an Outlook e-mail by dragging it and hovering over the Outlook icon in the taskbar to bring the window to the foreground. Once in the foreground, drop your file into the e-mail to attach it. You can also customize your taskbar with your favorite apps from Start’s All apps list by dragging and dropping over the taskbar to pin them. You can also drag and drop to the desktop via “Show desktop” at the very right corner of the taskbar.