why is the $this->db not available in a certain module?

I recommend you learn about PHP and OOP.

$this->load->database() creates a database object of CI3 and set it to the property $db ($this->db)
in the controller. Within CodeIgniter's Models, you can also use $this->db.
It is the functionality of CodeIgniter.

If you want to use a database object of CI3 in your MyExport6765.php,
you need to create a database object in it or inject the db object into it.

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