http://php.net/manual/en/function.ob-start.php
> The [output_callback] function will be called when the output buffer is flushed (sent) or cleaned (with
> ob_flush(), ob_clean() or similar function) or when the output buffer is flushed to the browser at the end of the
> request.

1. When you echo "Hello there", the callback is *not invoked immediately*
2. ob_get_contents returns "Hello there" back
3. ob_clean sends "Hello there" to the callback, which replaces using "World", but the result is discarded
4. You echo the original "Hello there" again
5. ob_end_flush sends the new "Hello there" to the callback, which replaces using "What?", and the result is sent

Is there a reasonable use case behind this problem? Because otherwise what you should be doing is simply
  ob_start('a::parse_output');
  echo "Hello there";
  ob_end_flush();

Well, it makes sense. So I should use the output callback phase parameter to check.
Could you tell me which is the phase which runs only once when the output buffer closed completely?

class a {

    private static $bug = 'World';
    

    public static function parse_output($buffer, $phase) {

        if ( $phase & PHP_OUTPUT_HANDLER_FINAL ){

            $buffer = str_replace('there', self::$bug, $buffer);
    
            self::$bug = 'What?';
        }

        return $buffer;
    }
}

FINAL is the one.