On my archives page, I can’t see my custom post types catergories

For this to work you need to register in your custom post type.

'has_archive' => true,

Or if you’re using CPT UI or the like, there are settings to enable the WP Category.

Mind you, this will give it access to the global category which is also used by Posts. Otherwise you’ll want to register a custom taxonomy.

For your current query:

Remove ‘category’ from your code above, and before you register your post type you need to register your tax. E.g:

register_taxonomy('topics', 'work', array(
    'label' => __( 'Topics' ),
));