OK, now that I have found the answer, this is a little trivial. But I think this is a cool thing to know, and currently it is not tied to the search bar in the title, so:
Pycharm allows you to view a sub window attached to the pycharm background as a native window, other than the main pycharm window. Just click on the small gear symbol in the upper right corner of the sub window and select βwindow modeβ. Now you can simply move this window to another desktop.
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