WP hook to add custom content after the_title()

You need to introduce your own hook (that’s how I’d do it).
I’ve added a custom hook in the following snippet:

<header class="entry-header alignwide">
    <?php the_title( '<h1 class="entry-title">', '</h1>' ); ?>
    <?php do_action('custom_after_title_hook'); ?>
    <?php twenty_twenty_one_post_thumbnail(); ?>
</header>

In order for this to work, you need to have:

  1. Access to the header.php
  2. OR overwrite it in a child-theme.

Last thing is easy: just call the function in your functions.php file like this:

<?php

    function custom_after_title_hook(){

         $some_var="<span>some text after title</span>";

         return $some_var;
    }
    add_action('my_custom_action', 'custom_after_title_hook');

?>

You can also add this to a plugin, but then you need to work with ‘template_include’.