Filter the loop by categories using checkbox form

Question

I feel I'm close in solving this issue but kinda hit a wall.

I have a loop on the examlpe.com/blog site and I'd like to be able to filter it using the category checkboxes.

Here is my loop

<h3 class="header__heading | u-margin__bottom--400">Latest posts</h3>
  <div class="grid__col--span-2">
    <?php
        $latestPostLoop = new WP_Query(array('posts_per_page' => 6));
        while ($latestPostLoop->have_posts()) : $latestPostLoop->the_post(); ?>
    <?php   $ids[] = get_the_ID(); ?>
    <?php include(locate_template('partials/summary--article.php', false, false)); ?>
    <?php endwhile; ?>
    <?php wp_reset_postdata(); ?>
  </div>

The form:

<?php
// Get all "Topic" terms
$category_terms = get_terms(
  array(
    'taxonomy'   => 'category',
    'hide_empty' => false,
  )
);



// Get active taxonomy filters
$category_selected = get_query_var('category');
if ( ! is_array($category_selected)) {
  $category_selected = array($category_selected);
}

$archive = get_post_type_archive_link('post');

?>
<form action="<?php echo esc_url($archive); ?>" method="get">

   <div>
    <input type="hidden" name="post_type" value="post">
    <?php
    $search = trim(get_search_query());
    if ( ! empty($search)) {
    ?>
    <input type="hidden" name="s" value="<?php echo esc_attr($search); ?>">
    <?php } ?>

  <fieldset class="form__fieldset">
    <legend class="form__legend">Category</legend>
     
    <div class="form__item--checkbox">
    <?php 
      $selected = empty($category_selected) || empty($category_selected[0]) ? 
       'checked="checked"' : '';?>
       <input type="checkbox" value="" id="checkbox-category-1" class="form__checkbox" 
        name="category" <?php echo $selected ?>>
       <label for="checkbox-category-1" class="form__label">All</label>
    </div>

      <?php
      $count = 2;
      foreach ($category_terms as $term) {
        $selected = in_array($term->slug, $category_selected) ? 'checked="checked"' : '';?>

      <div class="form__item--checkbox">
        <input type="checkbox" value="<?php echo esc_attr($term->slug); ?>" id="checkbox-topic- 
       <?php echo $count; ?>" name="category[]" class="vf-form__checkbox" <?php echo $selected ?>>             
        <label for="checkbox-topic-<?php echo $count; ?>" class="vf-form__label"><?php echo 
      esc_html($term->name); ?>
      </label>
    </div>

      <?php 
        $count++;
      } ?>
      </fieldset>

    <button class="button" type="submit">
      <?php esc_html_e('Apply filter', 'theme'); ?>
    </button>

  </div>
</form>

After submitting the form the URL I see is .../blog/?post_type=post&category=category name

However, this doesn't have any effect and I can see all the posts.

Any help much appreciated!