At least it got a bit better with 5.57 and Windows 7:
The bar still disappears in the background after full screen applications were launched, but it's at least possible to bring the window to front for a short time, when you click on the taskbar preview thumbnail.
Anyway Winamp will go to the background again as soon as another window is selected.
To bring it permanently back to front again, you still have to refresh the Winamp window by pressing F5.
Useless for me because dragging and dropping files on the Winamp window still won't work this way, but maybe this new possibility is useful for someone else at least.
Or maybe that was already possible with 5.56 or before and I just never noticed it...