This would cause the downloaded file to have incorrect file extension because such services don't configure the Content-Disposition header properly, and you still may have lots of improperly named files unless you realize that the file content doesn't match its extension.
That seems more likely. I still hate webp.
Does it actually request the image that it already downloaded again to save it to a file? Seems rather silly?
No, the server is just sending the file named 'foo.jpg', but encoded as a webp with webp mime type, so when you save the file it defaults to the webp extension cause it ends up treating the filename as a blob of text without an expected extension for the file type.
No, this is not what’s happening. Or at least not the phenomenon I am discussing.
Annoyingly, this doesn't work for a whole lot of websites that insist on serving webp, they just ignore the header. Some of them have bespoke workarounds like adding ?format=original on fandom wikis, with some the server will just never serve you anything other than webp.