How to deliver webp format of images to WP REST API

I use WP Offload Media Lite plugin to offload upload image to S3. I use raw S3 URL (not CDN) and choose remove file in server option. Then I use EWWW Image Optimizer plugin to convert image on S3 to .webp format. I run bulk optimize and there are .webp copies on S3. Then I choose JS Webp Rewriting to delivery .webp to my site (because I use Nginx) and it works well. But my partner request me deliver .webp to WP Rest api too. Because when he call : (GET) , it returns response that has only .jpeg, not .webp. I’m not familiar with WP rest api. How could I do that?