function webp_upload_mimes($existing_mimes) {
$existing_mimes['webp'] = 'image/webp';
return $existing_mimes;
}
add_filter('mime_types', 'webp_upload_mimes');

function webp_is_displayable($result, $path) {
if ($result === false) {
$displayable_image_types = array( IMAGETYPE_WEBP );
$info = @getimagesize( $path );

if (empty($info)) {
$result = false;
} elseif (!in_array($info[2], $displayable_image_types)) {
$result = false;
} else {
$result = true;
}
}

return $result;
}
add_filter('file_is_displayable_image', 'webp_is_displayable', 10, 2);