add_post_type_support( 'page', 'excerpt' );

function posts_where_excerpt_not_empty( $where ) {
    // on the home page or a category page
    if(is_home() || is_category()){
    $where .= " AND post_excerpt != '' ";
    }
    return $where;
}
add_filter( 'posts_where' , 'posts_where_excerpt_not_empty' );

function my_post_queries( $query ) {
  // not an admin page and is the main query
  if (!is_admin() && $query->is_main_query()){
    // on the home page or a category page
    if(is_home() || is_category()){
      $query->set('post_type', array('post', 'page'));
    }
  }
}

add_action( 'pre_get_posts', 'my_post_queries' );