<?php
/**
 * The template for displaying taxonomy faq_cat
 */

get_header(); ?>

<div class="wrapper" id="manual-archive">
    
    <div id="content" class="container-fluid">
	
		<div class="row">
		 
			<div class="col-12 col-md-8">
		
				<section id="breadcrumbs_top_content">						
					<?php
					if ( function_exists('yoast_breadcrumb') ) {
					  yoast_breadcrumb( '<p id="breadcrumbs">','</p>' );
					}
					?>	
				</section>
		
				<div class="content row">
				
					<div id="full-width" class="col-12 content-area">		
					  
						<main id="main" class="site-main" role="main">
						
							<div class="gazette_archive_wrapper">					
							
								<?php // Output all Taxonomies names with their respective items
									$current = $wp_query->get_queried_object();
									$current_term_id = $current->term_id;
									$current_name = $current->name;
									$current_taxonomy = $current->taxonomy;
									$current_parent = $current->parent;
									
								//$terms = get_terms('manual_cat');
								
								$terms = get_terms( array(
										'taxonomy'      => $current_taxonomy,
										//'child_of'      => $current_term_id,
										//'hide_empty'    => false,
										//'parent' => 0,
									) );
								
								foreach( $terms as $term ):
								
								?>                          
									  <section class="manual-header">
									  
										<h3><?php echo $term->name; // Print the term name ?></h3>
									
										</section>
									  
									  <?php                         
										  $posts = get_posts(array(
											'post_type' => 'manual',
											'tax_query' => array(
												array(
													'taxonomy' => $term->taxonomy,
													'field'    => 'slug',
													 'terms'   => $term->slug,
													//'operator ' => 'IN',
													 )
												),
											'posts_per_page'	=> -1,
											'order' => 'ASC',
										  ));
										  
										  foreach($posts as $post): // begin cycle through posts of this taxonmy
											
											setup_postdata($post); //set up post data for use in the loop (enables the_title(), etc without specifying a post ID)
									  ?>        
										  <section class="manual-entry">
										  
												<a rel="nofollow" href="<?php the_permalink(); ?>"><?php the_title(); ?></a>
											
										  </section>  
										  
										<?php endforeach; ?>  
										
								<?php endforeach; ?>
															
							
							</div><!-- .artcile_archive_wrapper-->

						</main><!-- #main -->
					   
					</div><!-- #primary -->

				</div><!-- .content -->
			
			</div><!-- .row -->
			
		</div><!-- .row -->
        
    </div><!-- .container-fluid -->
    
</div><!-- .wrapper -->

<?php get_footer(); ?>

Solution - 1

This will help you. https://developer.wordpress.org/reference/functions/get_term_children/ get_term_children( int $term_id, string $taxonomy ) This will Merge all term children into a single array of their IDs. Then pass that array into your post type tax_query with field "term_id"

Solution - 2

Instead of doing this, I would use the hook: pre_get_post. I would change the default query to include there also the term children into the tax query that is being executed.