FindImageShapes for "Rectangles"?

Question

I need to find affine projections of rectangular content in an image, e.g., paintings, postcards, posters, etc.

I was surprised that FindImageShapes only supports lines, circles, and eclipses!

Is there a built-in way to do this in v14? And if not, how to extend FindImageShapes?

Example:

img = Import@
  "https://www.wolframcloud.com/obj/ffcb49f6-e44c-4c2b-a2e3-3cdc842ae085"
FindImageShapes[img, "Rectangle"]

First and worst attempt:

comp = ImageSegmentationComponents[img];
Colorize@comp

area = Times @@ ImageDimensions[img];
rects = SortBy[
   ComponentMeasurements[
    comp, {"BoundingBox", "Rectangularity", 
     "Area"}], -#[[2, 2]]^(1/2) + (#[[2, 3]]/area) &];
HighlightImage[img, {Red, Rectangle @@@ rects[[1 ;; UpTo[15], 2, 1]]}]