How to make a transition through navigations (categories)?

Question

WordPress

There are custom categories (there are several of them)

<ul class="two__ul">
  <?php 
    $categories = get_categories( [
      'orderby'            => 'include',
  'order'              => 'ASC',
  'style'              => 'list',
  'show_count'         => 0,
  'hide_empty'         => 1,
  'child_of'           => 0,
  'exclude'            => '',
  'include'            => '4,5,6,7,8,9,10',
  'hierarchical'       => true,
  'title_li'           => __( '' ),
  'number'             => NULL,
  'echo'               => 1,
  'depth'              => 0,
  'pad_counts'         => 0,
  'taxonomy'           => 'category',
  'walker'             => 'Walker_Category',
    ] );

    if( $categories ) {
      foreach( $categories as $cat ) {

    ?>
      <li class="tu__li">
        <a  class="nav-link "
          href="<?php echo get_category_link($cat->term_id); ?>"
         >
          <?php echo $cat->name; ?>
        </a>
      </li>
  <?php
      }
    }
  ?>
</ul>

They are my menus, I want to make a transition on the same page by category. In fact, I go to another page (that is, to the page of the selected categories)
site.abc (click on the categories) --> site.abc/?cat=5 (5 here is the ID of the categories), I don’t understand which file (template ) it refers to I WANT to give the categories the same template as the main one.

In general, I found a solution, but I do not think that it is correct. I created a category.php file in the theme and copied my main (main page) template there