I noticed that the new profile design keeps the access ratio of most images, so I got curious, made a 40000 x 1 pixels PNG and set it up as a profile picture to see what would happen.
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This really seems to be working as intended. You uploaded a large image, and it was scaled as gracefully as possible to fit the container. It just so happens that, because of math, that makes it invisible.
If there is a bug here, it's that you're allowed to upload an image with such an absurd aspect ratio in the first place, or that the algorithms for handling non-square profile images are different between the profile page and the user box on the site (I've certainly seen cases where profile images look correct in one but not the other).