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How to split two interscting polygons by the average linestring of the shared area (QGIS / python shapely)

I have two polygons, POLYGON((-5 -5,-5 5,5 5,5 -5,-5 -5)) POLYGON((1 1, 1 7, 7 7, 7 1, 1 1)) and wish to split them evenly. The result should be a split along the red marked line. I'm using ...