Hi Jon,
Unfortunately, there is no support for webp from Kentico just yet. If you feel it's necessary please feel free to raise this as idea on their roadmap page here. I've posted this as a feedback a few times in the past, but if there will be more voices needing this feature I'm sure it will be implemented.
However even without Kentico's implementation of webp support there are a couple of things you can do still:
- Implement image optimization, here and here are the articles how I've done it. It will still remain JPG or PNG, but will be much more optimised and quite close to webp (at least google page speed will stop deducting the score, but will still be showing you the warning on images)
- Make use of the CDN for images. Some CDNs like Cloudflare allow image optimization on the fly. You simply turn this feature on the CND and it will start optimizing and caching the images coming from your website.