The supported image file types are defined in the function qa_upload_file() (located in qa-include/app/upload.php). To allow upload of .webp files you need to override (basically re-implement) that function in a custom plugin.
Changing core files is discouraged, so do not edit the original file. Your modifications would be lost when you update Q2A and you would have to re-apply them.
I don't think that just allowing the upload is sufficient, though. I expect you'll also need set the proper content type (image/webp) for the uploaded files to be displayed correctly. The respective code seems to be located in qa-include/qa-blob.php and currently only supports JPEG, PNG, GIF, PDF and Flash, and defaults to application/octet-stream for everything else. AFAICS that code doesn't support overriding, so you would have to resort to modifying a core file there (which, again, is not recommended).