Additional featured post on first page

If I understand your goal correctly, I would create two queries. The first will retrieve only the featured post. We’ll display that post on the first page only and store its ID to use later. Then, a second query will get all of the remaining posts.

// first query to retrieve the featured post
$featured_post_id = 0; // later we'll store the featured post's ID here
if(!is_paged()){ // ensure we only see the feature post on the first page
    $first_args = array(
        'post_type'      => array('post'), // change to custom post type if using one
        'post_status'    => array('publish'), // only get the latest published post
        'posts_per_page' => 1, // we'll only get one post
        'cat'            => 666, // put the ID of the 'featured' category here
    );

    $first_query = new WP_Query( $first_args );
    if($first_query->have_posts()) {
        while($first_query->have_posts()) {
            $first_query->the_post();
            $featured_post_id = get_the_ID();
            // your code for displaying the featured post here
        }
    } else {
        return;
    }
}

// second query to retrieve remaining posts (excluding featured post from above)
$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
$second_args = array(
    'post_type'         => array('post'),
    'post_status'       => array('publish'),
    'posts_per_page'    => get_option( 'posts_per_page' ), // will retrieve number of posts based on value set in WordPress's admin > Settings > Reading
    'paged'             => $paged, // use pagination
    'post__not_in'      => array($featured_post_id), // exclude featured post from first query
);

$second_query = new WP_Query( $second_args );
if($second_query->have_posts()) {
    while($second_query->have_posts()) {
        $second_query->the_post();
        // your code for displaying remaining posts here
    }
} else {
    return;
}
the_posts_pagination(); // your pagination code here