Add Taxonomy Term to a Node's Breadcrumb in Drupal 8

Breadcrumbs.php

<?php
// src/Breadcrumbs.php

namespace Drupal\modulename;

use Drupal\Core\Breadcrumb\BreadcrumbBuilderInterface;
use Drupal\Core\Routing\RouteMatchInterface;

use Drupal\Core\Breadcrumb\Breadcrumb;
use Drupal\Core\Link;
use Drupal\Core\StringTranslation\StringTranslationTrait;
use Drupal\node\NodeInterface;

/**
 * Class Breadcrumbs.
 *
 * @package Drupal\modulename
 */
class Breadcrumbs implements BreadcrumbBuilderInterface {

  use StringTranslationTrait;

  /**
   * {@inheritdoc}
   */
  public function applies(RouteMatchInterface $route_match) {
    return $route_match->getRouteName() == 'entity.node.canonical'
    && $route_match->getParameter('node') instanceof NodeInterface;;
  }

  /**
   * {@inheritdoc}
   */
  public function build(RouteMatchInterface $route_match) {

    $node = $route_match->getParameter('node');
    $breadcrumb = new Breadcrumb();

    // By setting a "cache context" to the "url", each requested URL gets it's own cache.
    // This way a single breadcrumb isn't cached for all pages on the site.
    $breadcrumb->addCacheContexts(["url"]);

    // By adding "cache tags" for this specific node, the cache is invalidated when the node is edited.
    $breadcrumb->addCacheTags(["node:{$node->nid->value}"]);

    // Add "Home" breadcrumb link.
    $breadcrumb->addLink(Link::createFromRoute($this->t('Home'), '<front>'));

    // Given we have a taxonomy term reference field named "field_section", and that field has data,
    // Add that term as a breadcrumb link.
    if (!empty($node->field_section->entity)) {
      $breadcrumb->addLink($node->field_section->entity->toLink());
    }
    return $breadcrumb;
  }
}

modulename.services.yml

# modulename.services.yml
services:
  modulename.breadcrumbs:
    class: Drupal\modulename\Breadcrumbs
    tags:
      - { name: breadcrumb_builder, priority: 100 }

If you also want the parents you can replace

    if (!empty($node->field_section->entity)) {
      $breadcrumb->addLink($node->field_section->entity->toLink());
    }

with

    if (!empty($node->field_section->entity)) {
      $term = $node->field_section->entity;
      $storage = \Drupal::service('entity_type.manager')
        ->getStorage('taxonomy_term');
      $parents = $storage->loadParents($term->id());

      if (!empty($parents)) {
        foreach ($parents as $index => $parent) {
          $breadcrumb->addLink($parent->toLink());
        }
      }

      $breadcrumb->addLink($term->toLink());
    }

Thank you all, here is a slightly more parametrized theme code version for non-node entities with taxonomy parents:

/**
 * Implements hook_system_breadcrumb_alter().
 */
function THEMENAME_preprocess_breadcrumb(array &$vars) {
  // proper taxonomy breadcrumbs for Commerce Products through field_category
  $entity_type = 'commerce_product'; // TODO: change or verify
  $taxonomy_field_name = 'field_category'; // TODO: change or verify

  if (($entity = \Drupal::routeMatch()->getParameter($entity_type)) && $vars['breadcrumb']) {
    $cache_tag = "{$entity_type}:{$entity->product_id->value}"; // TODO: change or verify

    $breadcrumb = &$vars['breadcrumb'];
    if (!empty($entity->$taxonomy_field_name->entity)) {
      $node_url = array_pop($breadcrumb);

      $term = $entity->$taxonomy_field_name->entity;
      $storage = \Drupal::service('entity_type.manager')
        ->getStorage('taxonomy_term');
      $parents = $storage->loadParents($term->id());
      if (!empty($parents)) {
        foreach ($parents as $index => $parent) {
          array_push($breadcrumb, $parent->toLink());
        }
      }
      array_push($breadcrumb, $term->toLink());

      array_push($breadcrumb, $node_url);

      // Implementing Cache.
      $vars['#cache']['contexts'][] = "url.path";
      $vars['#cache']['tags'][] = $cache_tag;
    }
  }
}

If you also want the parents you can replace

    if (!empty($node->field_section->entity)) {
      $breadcrumb->addLink($node->field_section->entity->toLink());
    }

with

    if (!empty($node->field_section->entity)) {
      $term = $node->field_section->entity;
      $storage = \Drupal::service('entity_type.manager')
        ->getStorage('taxonomy_term');
      $parents = $storage->loadParents($term->id());

      if (!empty($parents)) {
        foreach ($parents as $index => $parent) {
          $breadcrumb->addLink($parent->toLink());
        }
      }

      $breadcrumb->addLink($term->toLink());
    }

How would can I implement this solution to show the parents but using the YOURTHEME.theme preprocess function instead of the module? Thank you in advance.