How can I add HTML tags into menu title?
You need to tell drupal that the string is safe. When you use t() this is done  automatically. But this would make no sense here, because there is nothing to translate.

In this case you can use an untranslatable markup:

use Drupal\Core\Render\Markup;

function adminimal_theme_preprocess_menu(&amp;$vars) {
  if ($vars['menu_name'] === 'main') {
    if (isset($vars['items']['standard.front_page'])) {
      $vars['items']['standard.front_page']['title'] = Markup::create('&lt;i class="icon-home"&gt;&lt;/i&gt;');
    }
  }
}