Visualizing bounding box as polygon

Yes, it's the QuickWKT plugin (WKT = "Well-Known Text"). The bounding box would be treated as a polygon, and WKT would look like:

'POLYGON(x1 y1, x1 y2, x2 y2, x2 y1, x1 y1)'

Note that any polygon shape is possible, but coordinates following this model will generate a rectangle, which is what you want for a bounding box. You can't get away specifying only two corners, as you have in the question, you have to specify all four corners, and the first and last coordinates have to be the same. That's how WKT indicates that the polygon is closed.

A screenshot with the WKT for your first example:

See https://shapely.readthedocs.io/en/latest/manual.html#shapely.geometry.box

>>> import shapely.geometry
>>> bbox = (-125.056143, 31.8679566, -112.9017855, 42.4407224)
>>> polygon = shapely.geometry.box(*bbox, ccw=True)
>>> polygon
<shapely.geometry.polygon.Polygon object at 0x7fb070a9bf60>
>>> polygon.bounds
(-125.056143, 31.8679566, -112.9017855, 42.4407224)
>>> polygon.wkt
'POLYGON ((-112.9017855 31.8679566, -112.9017855 42.4407224, -125.056143 42.4407224, -125.056143 31.8679566, -112.9017855 31.8679566))'

For the example data given:

>>> bbox1 = (-32.61442167739459, -32.017601026186576, 13.015663782506067, 13.428145228091406)
>>> bbox2 = (-38.6102467739459, -38.017601026186576, 33.01563382506067, 33.624945228091406)
>>> polygon1 = shapely.geometry.box(*bbox1, ccw=True)
>>> polygon2 = shapely.geometry.box(*bbox2, ccw=True)
>>> polygon1.bounds
(-32.61442167739459, -32.017601026186576, 13.015663782506067, 13.428145228091406)
>>> polygon2.bounds
(-38.6102467739459, -38.017601026186576, 33.01563382506067, 33.624945228091406)
>>> polygon1.wkt
'POLYGON ((13.01566378250607 -32.01760102618658, 13.01566378250607 13.42814522809141, -32.61442167739459 13.42814522809141, -32.61442167739459 -32.01760102618658, 13.01566378250607 -32.01760102618658))'
>>> polygon2.wkt
'POLYGON ((33.01563382506067 -38.01760102618658, 33.01563382506067 33.62494522809141, -38.6102467739459 33.62494522809141, -38.6102467739459 -38.01760102618658, 33.01563382506067 -38.01760102618658))'