WooCommerce HTML after short description if product is in specific category

Woocommerce’s product categories are custom taxonomy terms, so you need to use the taxonomy functions (eg, has_term()) rather than WordPress’ category ones.

function filter_woocommerce_short_description( $post_excerpt ) {
    global $post;
    if ( has_term( "term-name", "product_cat", $post->ID ) ) {
        $post_excerpt .= "<br/>" . "Test";
    }
    return $post_excerpt; 
};
add_filter( 'woocommerce_short_description','filter_woocommerce_short_description',10, 1 );