How to fix duplicate posts in wordpress?

Question

WordPress

Hello! The bottom line is that there are repetitions on the output page of the records. as I understand it, they are because of the Show more button. Here is the code that outputs the entries:

<div class="b-blog-flow_flow" id="blog-posts">
            <?
            while ($posts->have_posts()) {
                $posts->the_post(); ?>
                <div class="b-blog-flow_item">
                    <div class="b-blog-flow_item-image-wrap">
                        <?php echo get_the_post_thumbnail(null, 'blog-thumb'); ?>
                    </div>
                    <div class="b-blog-flow_item-text">
                        <div class="b-blog-flow_item-date"><?php the_date('d.m.Y'); //echo get_the_date('h:i  |  G F Y');?></div>
                        <div class="b-blog-flow_item-content">
                            <div class="b-blog-flow_item-title"><?echo the_title();?></div>
                            <div class="b-blog-flow_item-short-text"><?echo the_excerpt();?></div>
                        </div>
                        <a class="e-more-link b-blog-flow_item-readmore" href="<? echo get_permalink();?>">Читать пост</a>
                    </div>
                </div>
                <?
            }
            ?>
        </div>
        <?php if ($total > $cnt) : ?>
        <div class="b-works-flow_more-button-wrap">
            <div class="e--button v--height-1 v--size-1 v--type-1 js-show-more">
                <div class="e--button__link">Показать больше</div>
            </div>
        </div>
        <?php endif; ?>

Here is the script that runs when you click on the Show more button:

<script>
    var cat = <?php echo $category ?>;
    var total = <?php echo $total ?>;
    var page = 2;
    $(function(){
      $('.js-show-more').click(function(){
          var params = {
              'page': page,
              'cat': cat,
          };
          var data  = jQuery.param(params);
          var action = 'getblogposts';
          sendForm(action, data, function (answer) {
              page++;
              $('#blog-posts').append(answer);
              if (($('#blog-posts .b-blog-flow_item').length)>=total) $('.b-works-flow_more-button-wrap').remove();
          });
      });
    })
</script>

Here is the php code for displaying the entry after clicking Show more:

function show_more_posts(){
    $nonce = $_POST['nonce'];
    if (!wp_verify_nonce($nonce,'email-nonce')) die('bad request');
    $category = intval($_POST['cat']);
    $page = intval($_POST['page']);
    $query = [
        'cat' => $category,
        'posts_per_archive_page' => 5,
        'paged' => $page
    ];

    $posts = new WP_query();
    $posts->query($query);

    while ($posts->have_posts()) {
        $posts->the_post();
        ?>
        <div class="b-blog-flow_item">
            <div class="b-blog-flow_item-image-wrap">
                <?php echo get_the_post_thumbnail(null, 'blog-thumb'); ?>
            </div>
            <div class="b-blog-flow_item-text">
                <div class="b-blog-flow_item-date"><?echo get_the_date('G F Y');?></div>
                <div class="b-blog-flow_item-content">
                    <div class="b-blog-flow_item-title"><?echo the_title();?></div>
                    <div class="b-blog-flow_item-short-text"><?echo the_excerpt();?></div>
                </div>
                <a class="e-more-link b-blog-flow_item-readmore" href="<? echo get_permalink();?>">Читать пост</a>
            </div>
        </div>
    <?php }
 die();
}

I can not figure out how to correct the code so that the entries do not repeat?