I can’t choose the custom taxonomy in my custom post type on Gutenberg

As Gutenberg does nearly everything over REST-API, you will have to update your register_taxonomy to be shown in REST, as the default value for show_in_rest in register_taxonomy is false.

So, you update your $args array in the function custom_taxonomy and add

'show_in_rest' => true

and you should be fine.

Happy Coding!