Override contrib module's template for an admin module

I need to override a contrib module's template for an admin module. For example, the webform_composite module has hook_theme() in its module file.

/**
 * Implements hook_theme().
 */
function webform_composite_theme() {
  return [
    'webform_composite' => [
      'render element' => 'element',
    ],
  ];
}

and a template in its templates folder at

modules/contrib/webform_composite/templates/webform-composite.html.twig

Changes made to the template print on the webform. I don't want to make changes to the module's template and I don't want to make a sub-theme of the admin theme. I want to override the contrib module's template in my custom module.

In my custom module, hook_theme() is like this:

/**
 * Implements hook_theme().
 */
function my_module_theme($existing, $type, $theme, $path) {
  return [       
    'webform_composite__custom' => [
      'base hook' => 'webform_composite',
    ],
  ];
}

And hook_theme_suggestions_alter() is like this:

/**
 * Implements hook_theme_suggestions_alter().
 */
function my_module_theme_suggestions_alter(array &$suggestions, array $variables, $hook) {
  if ($hook === 'webform_composite') {
    $suggestions[] = $hook . '--' . 'custom';
  }
}

as well as adding a template in modules/custom/my_module/templates/webform-composite--custom.html.twig

This adds my template but not as an override since webform-composite.html.twig still has the x.

<!-- THEME DEBUG -->
<!-- THEME HOOK: 'webform_composite' -->
<!-- FILE NAME SUGGESTIONS:
   * webform-composite--my-award.html.twig
   * webform-composite--custom.html.twig
   x webform-composite.html.twig
-->
<!-- BEGIN OUTPUT from 'modules/contrib/webform_composite/templates/webform-composite.html.twig' -->

How do I override a contrib module's template for an admin module?

Changing '--' to __ in the $suggestions array fixed the problem per this core issue: hook_theme_suggestions_alter does not work for hyphens

Here's the working code:

/**
 * Implements hook_theme().
 */
function my_module_theme($existing, $type, $theme, $path) {
  return [
    'webform_composite__custom' => [
      'base hook' => 'webform_composite',
    ],
  ];
}

/**
 * Implements hook_theme_suggestions_alter().
 */
function my_module_theme_suggestions_alter(array &$suggestions, array $variables, $hook) {
  if ($variables['theme_hook_original'] == "webform_composite") {
    $suggestions[] = $hook . '__' . 'custom';
  }
}

Now the debug reports:

<!-- THEME DEBUG -->
<!-- THEME HOOK: 'webform_composite' -->
<!-- FILE NAME SUGGESTIONS:
   * webform-composite--my-award.html.twig
   x webform-composite--custom.html.twig
   * webform-composite.html.twig
-->
<!-- BEGIN OUTPUT from 'modules/custom/my_module/templates/webform-composite--custom.html.twig' -->

The first template suggestion is from webform_composite.module -> hook_theme_suggestions_HOOK_alter().
The second template suggestion is my custom module.
The third template suggestion is from webform_composite.module -> hook_theme().

My custom template has the x and is the template read in by Drupal.