Using theme regions in custom module template.

Hello friends,

I recently purchased a theme for my Drupal website. Inside the theme folder there is -> templates/page--front.html.twig & page.html.twig

The a snippet of the <footer></footer> in page.html.twig looks as follows: 

    <footer class="site-footer">
      <div class="layout-container">
        {% if page.footer_first or page.footer_second or page.footer_third %}
          <div class="footer-top">
            <div class="footer-top-inner">
              {{ page.footer_first }}
              {{ page.footer_second }}
              {{ page.footer_third }}
            </div>
          </div>
        {% endif %}

        {% if page.footer_left or page.footer_right %}
          <div class="footer-bottom">
            <div class="footer-bottom-inner">
              {{ page.footer_left }}
              {{ page.footer_right }}
            </div><!-- /.footer-bottom-inner -->
          </div>
        {% endif %}
      </div>
    </footer>

I have a custom module that also has a templates folder. Do my custom module .html.twig files automatically extend/use the page.html.twig located inside my theme/templates? If so how would I got about adding sections like page.footer_left to the templates in my custom module?

I have tried adding a page variable in business_listing.module (business_listing is my custom module name):

function business_listing_theme($existing, $type, $theme, $path) {
  return [
    // business-listing-detail.html.twig
    'business_listing_detail' => [
        'variables' => ['data' => [], 'slides' => [], 'paths' => [], 'page' => []],
    ]

  ];

}

Then adding this via the render array of the function that loads my page in the controller like :

            $page['footer_left'] = "This should appear in the .footer-bottom div?";
            
            $build = [];
            $build['business_listing_detail'] = [
              '#theme' => 'business_listing_detail',
              '#data' => $record,
              '#slides' => $slides,
              '#paths' => $this->paths,
              '#page' => $page
            ];
            
            return $build;

But nothing appears? Any help and advice would be greatly appreciated <3 The theme is not my own, I am just trying to add pages that utilize its regions via a custom module.