How to fix ajax pagination when loading posts via ajax?

Question

WordPress

In general, I made a widget on the archive page that displays taxonomy elements and, when clicked, displays posts via ajax. The difficulty is that pagination breaks, which, for any request other than query_posts, refuses to appear at all, and with it loads the same posts that are already loaded (duplicates).
Post output and pagination code:

<div id="blog-list" <?php if ( $exm1_category_post_style == 'style_1' ){echo 'class="blog-category"';}elseif( $exm1_category_post_style == 'style_2' ){echo 'class="exm1-blog-posts-category"';}elseif( $exm1_category_post_style == 'style_3' ){echo 'class="img-featured"';}?>>
      <ul>		
      <?php if (have_posts()) : while (have_posts()) : the_post();?>								
        <li>					
        <?php if ( $exm1_category_post_style == 'style_1' ){	
          category_post_style1($author_show, $date_show);	
          }elseif( $exm1_category_post_style == 'style_2' ){
          category_post_style2($author_show, $date_show);
          }elseif( $exm1_category_post_style == 'style_3' ){
          category_post_style3($author_show, $date_show);	
          }?>			
        </li>
        <?php endwhile; else : ?>
          <div class="widget-title"><?php echo esc_html(get_option('exm1_no_match')); ?></div>
        <?php endif;?>
      </ul>
    </div>
    <?php $exm1_pagination_style = get_option('exm1_pagination_style');if($exm1_pagination_style =='ajax' || $exm1_pagination_style =='auto-load' ){?>
    <div class="pagination pagination-load-more <?php if($exm1_pagination_style =='auto-load'){echo esc_attr('auto-load');}?>">
      <?php $loadmoreword = get_option('exm1_word_load_more');
      next_posts_link(esc_html($loadmoreword), '' ); ?>
    </div>
    <!--pagination-->
    <?php } else { ?>
    <div class="pagination-simple">
      <?php exm1_pagination(); ?>
    </div>
    <!--pagination-simple-->
    <?php } ?>

The problem, it seems to me, is in the interaction of the script with next_posts_link , it is he who is responsible for the link that hangs on the button.
When loading the page with a normal transition, the link looks like mysite.com/category/news/page/2 ,
but after the posts are loaded via ajax it becomes like mysite.com/wp-admin/admin-ajax.php?action=get_cat&.. . .
I understand that the function receives the link in the wrong state, but js changes the address bar even before the ajax request is executed, and I can’t understand how it happens. How to fix it without crutches?