I often download images from the internet and in recent years WebP image format is very common.

WebP is a image format developed by Google: https://en.wikipedia.org/wiki/WebP.

Unfortunately it isn’t supported by default by many image viewers, including Eye Of Mate (my current image viewer).

Reading the issue about it on GitHub it seems that from last year it is possible to support it installing webp-pixbuf-loader.
GitHub issue: https://github.com/mate-desktop/eom/issues/104.

On Fedora it is just as simple as: sudo dnf install webp-pixbuf-loader.