By default .webp images cannot be posted to steam chat, however just renaming the extension to something else that is supported like .jpg allows the image to be uploaded and displayed in chat normally.
When downloading the image back from "steamusercontent" servers it is given the correct .webp extension.
This means that not only does steam chat recognize the incorrect .jpg extension and corrects it to a .webp extension, but that it also fully supports the format.

If uploading of .webp images to chat was restricted due to the old libWebP security issues then this trick easily circumvents the restriction.
If security is a concern then having steam try to guess and load files as something other then their stated format, especially as a format that isn't even said to be supported anywhere is generally not a good idea.
Otherwise if steam is up to date with patched libraries there is no reason to prevent direct upload for .webp images when .webm video that relies on the same libraries is officially supported already.