Eh, probably somewhere in between. I'm guessing it's a .webp being dragged, and for some reason iMessage (as a drag-and-drop drop-target) is claiming to be able to accept those, so Chrome doesn't bother to offer a JPEG representation, but instead just hands over the .webp as is. Then iMessage takes it, and realizes that it does not, in fact, know what to do with it.
The more interesting thing is that iMessage does deliver the image, when it's to an iMessage recipient. Just not when it's to an SMS recipient. So I'm registering my guess for the root cause as: the drop-target content-type capabilities for the iMessage chat window aren't being dynamically varied with the recipient type.
Cell carriers often drop Image sends that aren't GIF/PNG/JPG, so it makes sense that they'd drop WEBP. You could open a feedback report about the issue about not dynamically varying the drop target properties.
