The extension is called “webp” (for “Web progressive image format”) and not “wepd”. And this is already supported, see my demo site:
You have another issue on your website – it seems you use a plugin or theme which loads the gallery after the website has been loaded already. This is not supported at all – images must be part of the HTML code which is sent to the browser and must not be generated by some backend code which completeley ignores the WordPress content filters.
In addition: WordPress already adds the “lazy loading” attribute for images on a website and there is also an option in Lightbox for Photoswipe to add this if needed. HTTP/2 supports loading many objects within one single connection which also speeds up things a lot. So there is no need to hide images and create them just when scrolling down the website.
For example see my gallery which has a lot of images – and still loads in less then 2 seconds in Europe or about 3 seconds from North America according to Pingdom:
To speed up things even more you may want to use a CDN like Cloudflare. This is still better than having parts of your site only loaded when users scroll down the page. In the end they should see the images anyway.