Google has failed to convince any browser maker not using their entire Blink rendering engine (i.e. Opera) to implement support for WebP. It's been almost seven years, not what I'd call successful.
On the server side, if you're processing images to create multiple versions anyway (thumbnails, different sizes for mobile & desktop, etc.), throwing WebP versions in there is simple enough and should reduce bandwidth use. It's not worth doing if you're not fully automating image handling for other reasons.