With the taskbar displayed to the left, I hit the Windows key to bring up the search window. It displays to the left, immediately adjacent to the taskbar. But as soon as I start typing a search term the search window moves to the centre of the screen.
This behaviour does not occur when the taskbar alignment is centred. In this case the search window initially appears centred, and stays there.
It would be great if the search window could stay to the left when the taskbar is displayed to the left. Less desirably perhaps the search window could initially show centred and remain there regardless of the taskbar alignment. I would contend that having it move positions after beginning to type a search is a bit jarring.