Requested feature overview description.
WebP is an image format that supports alpha transparency and animation. It also produces smaller file sizes at the same quality than JPEG and GIF.
Why would it be useful?
It prevents generation loss from converting WebP files to JPEG, and large file sizes from converting files to PNG.
What part(s) of the site page(s) are affected?
Server side scripts (i guess).

Use the search next time.

topic #22506

Again, how many artists are uploading .webp anywhere?

If WebP Lossless Format can result in smaller files than PNG, then that would be a good reason to add it. I haven't researched that though.