How do I properly render links in custom item list when using complex render array?

I wish to use a custom item list template in a module that changes the <h3> tag. The items I am rendering are link render arrays.

When I use the default template, a link render array works correctly and outputs the links. When I use a custom template, the links no longer appear. Am I missing a step?

This is the code I am using in the module.

function mymodule_theme($existing, $type, $theme, $path) {
  return [
    'mymodule__item_list' => [
      'variables' => [
        'items' => [
          'attributes' => [],
          'value' => [],
        ],
        'title' => '',
        'list_type' => 'ul',
        'wrapper_attributes' => [],
        'attributes' => [],
        'empty' => NULL,
        'context' => [],
      ],
      'template' => 'mymodule--item-list',
    ],
  ];
}

The /templates/mymodule--item-list.html.twig template file contains the following code.

{#
/**
 * @file
 * Custom theme implementation for an item list.
 *
 * Available variables:
 * - items: A list of items. Each item contains:
 *   - attributes: HTML attributes to be applied to each list item.
 *   - value: The content of the list element.
 * - title: The title of the list.
 * - list_type: The tag for list element ("ul" or "ol").
 * - wrapper_attributes: HTML attributes to be applied to the list wrapper.
 * - attributes: HTML attributes to be applied to the list.
 * - empty: A message to display when there are no items. Allowed value is a
 *   string or render array.
 * - context: A list of contextual data associated with the list. May contain:
 *   - list_style: The custom list style.
 *
 * @see template_preprocess_item_list()
 *
 * @ingroup themeable
 */
#}
{% if context.list_style %}
  {%- set attributes = attributes.addClass('item-list__' ~ context.list_style) %}
{% endif %}
{% if items or empty %}
  {%- if title is not empty -%}
    <p><strong>{{ title }}</strong></p>
  {%- endif -%}

  {%- if items -%}
    <{{ list_type }}{{ attributes }}>
    {%- for item in items -%}
      <li{{ item.attributes }}>{{ item.value }}</li>
    {%- endfor -%}
    </{{ list_type }}>
  {%- else -%}
    {{- empty -}}
  {%- endif -%}
{%- endif %}

In the module, I assemble the link items into the unordered list using the following code.

// $foo and $bar are set from the code before this.
$commonlyUsedForItems = [];

foreach ($commonlyUsedfor as $name) {
  $url = Url::fromRoute('mymodule.page', [], [
    'query' => [
      'foo' => $foo,
      'bar' => $bar,
      'name' => $name,
    ],
  ]);

  // Create an array of link render arrays.
  $commonlyUsedForItems[] = [
    '#type' => 'link',
    '#title' => $this->t($name),
    '#url' => $url,
  ];
}

$commonlyUsedForRenderArray = [
  '#theme' => 'mymodule__item_list',
  '#type' => 'ul',
  '#title' => 'Commonly used for:',
  '#items' => $commonlyUsedForItems,
  '#attributes' => ['class' => 'commonlyUsedFor'],
  '#wrapper_attributes' => ['class' => 'container'],
];

The code above works correctly changing '#theme' => 'mymodule__item_list', to '#theme' => 'item_list',.

The code as it is kind of works, but it prints out empty bullet points.

I know I could revert the $commonlyUsedForItems array to markup and hardcode the HTML, but I am trying to keep HTML and PHP separated as much as I can.

Do you have any idea?