Template Overriding in Drupal 9 Modules

Copy template inside the templates directory in your module.
Then, reuse this snippet as per your overriden template.

Example:

If you want to override template: page--taxonomy.html.twig

1. Copy the template inside your modules templates directory.
2. Register it with your module preprocessor. i.e. <module_name>.module.

/**
 * Implements hook_theme().
 */
function hashtags_explore_theme() {
  return [
    'page__taxonomy' => [
      'template' => 'page--taxonomy',
      'base hook' => 'page',
    ],
  ];
}