How can I change the front-page title when front page is not /node?

It's not possible to change the front page title declaratively without adding a new module, such as the Metatag module. Drupal's core does not have this functionality. However, you can achieve this with a few lines of code implementing template_preprocess_html in your custom theme.

To achieve this dynamically in a subtheme, add this code to your preprocess_html function of your theme file or add if it doesn't exist.

function MYTHEME_preprocess_html(&$variables) {
  if (Drupal::service('path.matcher')->isFrontPage()) {
    $variables['head_title'] = [t('Hello World')];
  }
}

Note: Credit to @leymanx for the basis for the above code, which just needed a slight modification to update the title as originally asked, rather than just the portion of the before name of the site.

The default Frontpage is a view (admin/structure/views/view/frontpage/edit) showing a waterfall of all content that is Published and "Promoted to the Frontpage". By default, the Frontpage view's Title is "none" while the HTML Title tag is "Home | MySite.com".

So you can change the Title of the view there to e.g. "Start" and the HTML title will change to "Start | MySite.com".

If, instead of using the Frontpage view, you choose a node for your home page (e.g. "node/10 ), then you can name the page "Home" and the HTML title will become "Home | MySite.com".

If you don't want the title of the page showing up in the page's content area (but you do want it in the home page's HTML title tag), you can hide the title block in admin/structure/block/manage/yourtheme_page_title.

The Metatag module, along with Token, can also be used for this and general SEO enhancements, but you said you are trying to avoid that.

You can achieve this with a few lines of code implementing template_preprocess_html in your custom theme.

/**
 * Implements template_preprocess_html().
 */
function MYTHEME_preprocess_html(&$variables) {
  if (Drupal::service('path.matcher')->isFrontPage()) {
    $variables['head_title']['title'] = t('Hello World');
  }
}

You can use the Metatag module. It has a section for front page metatags, where you can set the title.