How do I turn CPT automatically also into category?

You could add a custom callback to the save_post_{$post->post_type} action, which fires after the defined type of post has been saved. (Use your CPT name in the place of the curly brackets placeholder) The callback recieves the saved post as its second parameter, ID being the first, from which you can get appropriate details (namely the title) for wp_insert_term() which you’d use for adding the new term.

The callback recieves boolean value as the third parameter, which tells you, if the save happens for a new post or an existing one, i.e. is an update. You should utilize this to prevent your callback from creating a new term every time the action is fired, but only for new posts.

Check out the docs, https://developer.wordpress.org/reference/hooks/save_post_post-post_type/ and https://developer.wordpress.org/reference/functions/wp_insert_term/, for more details on how to use the action and the function.

P.s. I’m sorry for not adding a code example. Adding one now is a bit difficult as I’m typing this on a mobile device.