Ok the only way I can think of getting around this problem is to check the broswer and serve up a .webp image if the browser supports it by replacing the file extention with .webp
$postId = $post->ID;
$patterns = array("/.jpg/", "/.jpeg/", "/.png/");
$thePostThumbUrl = get_the_post_thumbnail_url($postId, array(768,768));
if (strpos($_SERVER['HTTP_USER_AGENT'], 'Opera') || strpos($_SERVER['HTTP_USER_AGENT'], 'OPR/') || strpos($_SERVER['HTTP_USER_AGENT'], 'Chrome') && !strpos($_SERVER['HTTP_USER_AGENT'], 'Edge'))
$thePostThumbUrl = preg_replace($patterns, ".webp", $thePostThumbUrl);