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

I believe there is a function deviation. The code is self-explanatory: it must be used to connect to a database. Unlike $db = $this->db; which can only be used in Controllers/Models, since "$this->" cannot be used in a non-object context.
Although not recommended if you want to make a query outside the Model/Controller you can use it:

PHP Code:

$db = db_connect();
$query = $db->table('mytable')
// and so on ... 


https://codeigniter.com/user_guide/datab...cting.html

I insist: I'm talking about CodeIgniter 4!
This option, db_connect();, is exclusive to CI4.

https://codeigniter.com/userguide3/datab...cting.html