WP_Query is not received in Ajax

You have use ajaxurl when make post request – it’s right way but it also mean that now $wp_query, in your my__load__more() function, work with your.site/wp-ajax url instead of your.site/taxonomy. That’s why you couldn’t get category name from $wp_query->query_vars.

First, I use add_action( 'wp_enqueue_scripts', 'my__enqueue' ); for enqueue your scripts (see example below).

Second, I change arguments you pass to wp_localize_script() function. I offer get name of category when you add script to page instead of get it inside ajax handler:

add_action( 'wp_enqueue_scripts', 'my__enqueue' );
function my__enqueue(){
    wp_enqueue_script( 'my__load__more', get_template_directory_uri() . '/assets/js/load_more.js', array( 'jquery' ), '1.0.0', true );

    global $wp_query;
    $vardi      = $wp_query->query_vars;
    $category   = isset( $vardi[ 'category_name' ] ) ? $vardi[ 'category_name' ] : '';

    $ajaxurl    = admin_url( 'admin-ajax.php' );

    wp_localize_script( 'my__load__more', 'my__params', array(
        'ajaxurl'   => $ajaxurl,
        'category'  => $category,
    ) );
}

Of course, you could add parameter category in same way you add ajaxurl in your code:

wp_localize_script( 'my__load__more', 'my__category', $category );

Pay attention

If you are going to use array in wp_localize_script() function note that now you need use it in your js code as an object element, e.g., my__params.ajaxurl instead of ajaxurl

Third, we need to change your post call:

$.post(my__params.ajaxurl, // if you use array
{
    'action': 'my__load__more',
    'addNum': addNum,
    'getChoose': getChoose,
    'category': my__params.category, // pass category to handler
}

Fourth, and last, change handler:

function my__load__more(){
    // this is your handler beginning

    $args__load = array(
        'posts_per_page' => -1,
        'post_type'      => 'post',
        'post_status'    => 'publish',
    );

    if( !empty( $_POST[ 'category' ] ) ) $args__load[ 'category_name' ] = $_POST[ 'category' ];

    $articles = new WP_Query( $args__load );
    
    // this is your handler ending
}

Value in $_POST[ 'category' ] could be empty, so we no need to use it in our query. Sure, you could add it directly to $args__load array with other parameters without any if, as you want.

Hope it helps 😉