Hello WordPress StackExchange. What I'm trying to accomplish is producing numbered pagination for posts which are loaded via an ajax function. I have to make the numbered pagination work via ajax as well. Explanation of each code block below:

This function produces taxonomy terms which currently have posts assigned. Code resides in functions.php.

<?php
    function ee_event_categories() {
      $event_cats = get_terms( array(
        'taxonomy' => 'tribe_events_cat',
        'hide_empty' => true,
      ) );
    ?>
        <div class="filter-column category-block">
          <?php foreach ( $event_cats as $event_cat ) : ?>
            <button 
              data-taxonomy="<?php echo $event_cat->taxonomy; ?>" 
              data-slug="<?php echo $event_cat->slug; ?>"
              data-term-id="<?php echo $event_cat->term_id; ?>">
              <?php echo $event_cat->name; ?>
            </button>
          <?php endforeach; ?>
        </div>
    <?php
      $cat = ob_get_clean();
      return $cat;
    }
    add_shortcode( 'ee_event_categories', 'ee_event_categories' );
?>

Upon clicking on the resulting buttons from the previous function, a custom WP_Query runs and displays posts that match the criteria in the function below. This function resides in functions.php. I think I have to pass the $paged variable from the load_events_by_category() function into the javascript code. Unfortunately, I'm at a loss as to how to do it. Maybe the $paged variable needs to be applied as a second key / value pair in the wp_localize_script() declaration? Now I'm thinking out loud.

<?php
function load_events_by_category() {
  $paged = ($_POST['paged']) ? $_POST['paged'] : 1;
  $taxonomy = $_POST['taxonomy'];
  $slug = $_POST['slug'];
  $term_id = intval($_POST['term_id']);
    $category_events_args = array(
      'post_type'       => 'tribe_events',
      'posts_per_page'  => 4,
      'post_status'     => 'publish',
      'eventDisplay'    => 'custom',
      'order'           => 'ASC',
      'paged'           => $paged,
      'tax_query' => array(
        array(
          'taxonomy' => 'tribe_events_cat',
          'field'    => 'term_id',
          'terms'    => $term_id
        )
      )
    );
    $catquery = new WP_Query( $category_events_args );
    ob_start(); 
    if( $catquery->have_posts() ) : ?>
      <div class="this-weeks-events">
        <div class="featured-events-grid">
          <?php while ( $catquery->have_posts() ) : $catquery->the_post(); ?>
            <div class="featured-events-grid-child">
              <div class="event-date"
                data-taxonomy="<?php echo $taxonomy ?>"
                data-slug="<?php echo $slug; ?>" 
                data-term-id="<?php echo $term_id; ?>" 
                style="background:<?php echo the_field('event_category_background', $taxonomy . '_' . $term_id ); ?>"
              >
                <p class="event-day"><?php echo tribe_get_start_date( $event_id, false, 'D' ); ?></p>
                <p class="event-start-date" style="color:<?php echo the_field('event_date_color', $taxonomy . '_' . $term_id ); ?>"><?php echo tribe_get_start_date( $event_id, false, 'j' ); ?></p>
                <p class="event-month"><?php echo tribe_get_start_date( $event_id, false, 'F' ); ?></p>
              </div><!-- end div event-date -->

              <?php if( has_post_thumbnail() ) : ?>
                <div class="featured-image">
                  <a href="<?php echo the_permalink(); ?>"><?php the_post_thumbnail( 'full' ); ?></a>
                </div><!-- end div featured-image -->
              <?php endif; ?>
              <div class="featured-events-details-grid">
                <div><h2><a href="<?php echo the_permalink(); ?>"><?php the_title(); ?></a></h2></div>
                <div>
                  <i class="far fa-clock" aria-hidden="true"></i>
                  <?php echo tribe_get_start_time( $event_id ); ?>
                  -
                  <?php echo tribe_get_end_time( $event_id ); ?>
                  <?php if( tribe_is_recurring_event() ) : ?>
                    <p class="event-recurring"><img src="<?php echo get_stylesheet_directory_uri() . '/images/arrows-rotate.webp' ?>" alt="rotating arrow icon for weekly events" width="20" height="20" /> Weekly Event</p>
                  <?php endif; ?>
                </div>
              </div><!-- end div featured-events-details-grid -->
            </div><!-- end div featured-events-grid-child -->
          <?php endwhile; ?>
        </div><!--end featured events grid -->        
        <?php
          $nextpage = $paged+1;
          $previouspage = $paged-1;
          $total = $catquery->max_num_pages;
          $pagination_args = array(
            'base'                => '%_%',
            'format'              => '?paged=%#%',
            'total'               => $total,
            'current'             => $paged,
            'show_all'            => false,
            'end_size'            => 1,
            'mid_size'            => 2,
            'prev_next'           => true,
            'prev_text'           => __('<span class="prev" data-attr="'.$previouspage.'">&laquo;</span>'),
            'next_text'           => __('<span class="next" data-attr="'.$nextpage.'">&raquo;</span>'),
            'type'                => 'plain',
            'add_args'            => false,
            'add_fragment'        => '',
            'before_page_number'  => '',
            'after_page_number'   => ''
          );
          $paginate_links = paginate_links($pagination_args);

          if ($paginate_links) : ?>
            <div id='pagination' class='pagination'>
              <?php echo $paginate_links; ?>
            </div>
          <?php endif; ?>
      </div><!-- end div this weeks events -->
    <?php endif; ?>
    <?php wp_reset_postdata(); ?>
    <?php
      $content = ob_get_clean();
      echo $content;
      die();
}
add_action( 'wp_ajax_load_events_by_category', 'load_events_by_category' );
add_action( 'wp_ajax_nopriv_load_events_by_category', 'load_events_by_category' );
?>

I'm not sure if this is important but I'll include it anyway. It's how I'm using wp_localize_script, also located in functions.php.

<?php wp_enqueue_script( 'ajax-load-category-events', get_stylesheet_directory_uri() . '/dist/ajax-category-events.js', array( 'jquery' ), '1.0', true ); 
wp_localize_script( 'ajax-load-category-events', 'categoryevents', array(
  'ajaxurl'   => admin_url( 'admin-ajax.php' )
));
?>

And finally, here's the code in above javascript file.

(function ($) {
  $(".category-block button").on('click', function (e) {
    e.preventDefault();
    $.ajax({
      type: 'POST',
      url: categoryevents.ajaxurl,
      data: {
        action: 'load_events_by_category',
        taxonomy: $(this).data('taxonomy'),
        slug: $(this).data('slug'),
        term_id: $(this).data('term-id')
      },
      success: function (html) {
        $('#fl-main-content').find('#event_results .fl-rich-text').empty();
        $('#event_results .fl-rich-text').append(html);
      },
      error: function (error) {
        console.log("Error: ", error)
      }
    })
  });
})(jQuery);