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Older shapely versions (before OverlayNG) would have always given the second answer, with a LineString intersection output, without area. Newer shapely versions with OverlayNG unfortunately return an unexpected intersection in the first example, where the result geometry does not really intersect poly1. @dr-jts might be able to weigh in to say if this is expected or not:
If you are using Shapley 2+ with a modern GEOS (most are), then you can use the optional grid size to round the overlay coordinates, here using a very small grid size close to machine epsilon:
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