How to make multiple custom taxonomies sit under custom post type slug?

You commented, “As far as I can see rewrite is only possible for one taxonomy?“.

So no, that’s not true, it’s possible for every taxonomy. Just remember that each taxonomy should have a unique rewrite slug, so that it does not conflict with other permalinks (for other taxonomies and for post types like post, page, etc.). So for instance, if the topics taxonomy uses topics as the rewrite slug, then your types and industries taxonomies need to use a different rewrite slug. (If you really must use/share the same slug, it’s not impossible, but it’s not in scope of this answer)

Now if these are the permalink structures that you want:

• /resources/topics/<term slug> for the topics taxonomy
• /resources/types/<term slug> for the types taxonomy
• /resources/industries/<term slug> for the industries taxonomy

where an example permalink (URL) would look like this:

• https://example.com/resources/topics/security/ for a term with the slug security, in the topics taxonomy
• https://example.com/resources/types/article/ for a term with the slug article, in the types taxonomy
• https://example.com/resources/industries/accounting/ for a term with the slug accounting, in the industries taxonomy

Then just set the rewrite slug for your taxonomy to resources/<taxonomy>, like so:

(this is the actual code I tried & tested working with WordPress v6.1.1)

function my_register_post_types() {
    register_post_type(
        'resources', // post type name/slug
        array(
            'public'  => true,
            'rewrite' => array( 'slug' => 'resources' ),
            'labels'  => array(
                'name' => 'Resources',
                // other labels
            ),
            // other args
        )
    );
}

function my_register_taxonomies() {
    register_taxonomy(
        'topics',    // taxonomy name/slug
        'resources', // attach to this post type
        array(
            'public'       => true,
            'rewrite'      => array( 'slug' => 'resources/topics' ),
            'label'        => 'Topics',
            'hierarchical' => true,
            // other args
        )
    );

    register_taxonomy(
        'types',     // taxonomy name/slug
        'resources', // attach to this post type
        array(
            'public'       => true,
            'rewrite'      => array( 'slug' => 'resources/types' ),
            'label'        => 'Types',
            'hierarchical' => true,
            // other args
        )
    );

    register_taxonomy(
        'industries', // taxonomy name/slug
        'resources',  // attach to this post type
        array(
            'public'       => true,
            'rewrite'      => array( 'slug' => 'resources/industries' ),
            'label'        => 'Industries',
            'hierarchical' => true,
            // other args
        )
    );
}

However, you need to first register the taxonomies, and only after that, register your resources post type, if its rewrite slug is resources, which is the default value, or that the slug starts with resources/. Otherwise, your term permalinks would result in a 404 error page. :/

// Register the taxonomy first.
add_action( 'init', 'my_register_taxonomies' );

// Then the post type.
add_action( 'init', 'my_register_post_types' );

Also, be sure to flush the rewrite rules (i.e. re-save your permalinks), by simply visiting the Permalink Settings admin page.