No, a backward pawn doesn't need to be on a semi-open file to be considered backwards. Of course, a backwards pawn on a semi-open file is likely more vulnerable than if the file was closed (or a piece able to blockade the backward pawn weakness via interference).
Does a backward pawn has to be on an semi open filen?
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To be regarded as a backward pawn There seem to be no unity in literature. But I can be too stupid as well, never knows