Ok, but should the arc typically be able to be swept around a rectangle?
Yes, but the profile should lie on the miter plane when the path is closed AND the desired body is of type sheet.
Here's the final result:
The following steps show how to properly move your original arc to the miter plane. Create two normal work planes using the Normal to Curve at Point method, and create a work axis using the Intersection of Two Planes method.
Create a miter plane using the Angle to Plane around Edge method.
We want to project the original arc to the miter plane in the direction shown with the yellow arrow below. I will just use the Extrude feature for this projection.
Use the projected arc on the miter plane as the sweep profile. You should be able to select four edges for the sweep path.
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