Banding the sides of an image is called pillarboxing (as opposed to banding the top and bottom, i.e., letterboxing). Wikipedia's page refers to the technique you describe as "stylized pillarboxing" or "echo pillarboxing".
OK, so I didn't have a box of fascinating delicacies to try this out on -
I just had a box of eggs & some blueberries in the fridge, which I sat by the window-sill in direct but quite muted sunlight.
if you can't read it, it's because I flipped it left to right to better match the OP
It's by no means the perfect photo, just a quick example.
That looks to me more like noise, particularly chrominance noise, than posterization or banding. But the two things can look very similar at times, particularly if too much compression was used when converting to JPEG.¹ There are some noticeable compression artifacts near the edges between the red sleeve and the background.
When one underexposes a shot and ...
If you mean the very narrow plane of focus, it is possibly obtained with a tilt-shift lens where, instead of using the tilt that makes the focus plane cover the subject, they used the tilt that make the focus plane have a small intersection with the subject.
It's also possibly just a very wide aperture for a shallow depth of field.