WP_Query tax query part of slug

You can use below code to search in taxonomy. First using name__like in get_terms it will return all terms ids which have $keyword then that ids use in wp_query.

$termIds = get_terms([
    'name__like' => $keyword,
    'fields' => 'ids'
]);
$args = [
    'post_type' => 'movies',
    'tax_query' => [
        [
            'taxonomy' => 'actors',
            'field' => 'id',
            'terms' => $termIds,
        ]
    ]
];

$query_loop = new WP_Query($args);