YouTube embed parameters?

There’s always a filter you can use to hook into the output, see embed_oembed_html. Try this in a custom plugin or child theme’s functions file, it will add any other query strings to the iframe src attribute:

add_filter("embed_oembed_html", function( $html, $url, $attr ) { 
    parse_str(parse_url($url, PHP_URL_QUERY), $url);
    if ( $url ) {
        foreach ( $url as $q=>$v ) {
            preg_match('/src="https://wordpress.stackexchange.com/questions/250140/([^"]+)"https://wordpress.stackexchange.com/", $html, $src);
            if ( isset( $src[1] ) ) {
                $html = str_replace(
                    $src[1],
                    add_query_arg( array( $q=>$v ), $src[1] ),
                    $html
                );
            }
        }
    }
    return $html;
}, 10, 3);

Make sure there are no query strings you don’t want to add to the iframe src and skip them with a continue; in the loop.

Hope that helps.