Assign / update custom field value for all posts (How can I assign only to posts without custom field value?)

You can use meta_query parameter (and Query all posts where a meta key does not exist) to limit the query to only posts that have or don’t have a certain meta value.

$query = new WP_Query(array(
    'post_type' => 'post',
    'post_status' => 'publish',
    'posts_per_page' => -1,
    'meta_query' => array(
        array(
            'key' => 'your_meta_key',
            'compare' => 'NOT EXISTS',
        ),
    ),
    'no_found_rows' => true,
    'fields' => 'ids',
));

if ( $query->posts ) {
    array_walk(
        $query->posts,
        function($post_id, $index) {
            update_post_meta( $post_id, 'your_meta_key', 'meta_value' );
        }
    );
}

Also, depending on your hosting, you may want to set a limit to the posts_per_page and run the script multiple times (cronjob maybe?) instead of using -1 as the query for thousands of posts might crash the site or the execution time could run out.