An example of what the WP_Query() might look like to fetch all posts with the "LibTechGender" category that only have the "Link" post format.

LibTechGender_Fetch_Links_WP.php

/* 
Assuming a parent category called "LibTechGender" with sub-categories
like "Code of Conduct", "Impostor Syndrome," etc. Probably get more
nesty to separate by "Articles (Mine)" and "Articles (Others)," but
the point is it can be done with just categories.
*/

// Fetch articles about the "Code of Conduct"
$args = array(
  'post_type'     => 'post',
  'category_name' => 'code_of_conduct',
  'tax_query'     => array(
    
    'relation'    => 'AND',
    
    // Get LibTechGender Posts
    array(
      'taxonomy'  => 'category',
      'field'     => 'slug',
      'terms'     => array( 'libtechgender' )
    ),
    
    // and only Links
    array(
      'taxonomy'  => 'post_format',
      'field'     => 'slug',
      'terms'     => array( 'post-format-link' )
    )
  )
);

$the_query = new WP_Query( $args );

// Drop all of the LibTechGender "Code of Conduct" in a list
if ( $the_query->have_posts() ) :

  echo '<ul>';

	while ( $the_query->have_posts() ) {
		
		$the_query->the_post();
		
		  // Why "the_content()"? Presumably, the only thing in
		  // the post with the "link" format would be just the
		  // Title of the piece wrapped in a link. If that's it, 
		  // you can just post the whole content. If there's a
		  // corresponding paragraph or review, then this can be
		  // changed-up just to extract the link. This example
		  // assumes the lazy way :).
		  echo '<li>' . the_content() . '</li>';
	}
  
  echo '</ul>';
}

// Reset the Query
wp_reset_postdata();