Custom Page Template Category loop not functioning correctly

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Your foreach is closed prematurely.

foreach( $categories as $catergory ) {

    // query args
    $args = array(
        // args
    );
}

// generate the loop
$the_query = new WP_Query ( $args );

// output the loop
while ( $the_query->have_posts()) : $the_query->the_post(); 
    // Loop markup
endwhile;

wp_reset_postdata();

You’re saying:

  1. Step through each of the categories; for each category, add query results to $the_query.
  2. After stepping through the categories, output a loop for $the_query

So, you’re only ever going to display the loop for the last category in $categories.

Instead, you need to put the loop output inside your foreach loop:

foreach( $categories as $catergory ) {

    // query args
    $args = array(
        // args
    );

    // generate the loop
    $the_query = new WP_Query ( $args );

    // output the loop
    while ( $the_query->have_posts()) : $the_query->the_post(); 
        // Loop markup
    endwhile;

    wp_reset_postdata();
}

That way, you output a loop for each category, rather than just the last category.