I have the following data coming from my WP Rest API via https://cms.dboxcg.com/index.php/wp-json/wp/v2/taxonomies:

{
"category": {
    "name": "Categories",
    "slug": "category",
    "description": "",
    "types": [
        "post"
    ],
    "hierarchical": true,
    "rest_base": "categories",
    "_links": {
        "collection": [
            {
                "href": "https://cms.dboxcg.com/index.php/wp-json/wp/v2/taxonomies"
            }
        ],
        "wp:items": [
            {
                "href": "https://cms.dboxcg.com/index.php/wp-json/wp/v2/categories"
            }
        ],
        "curies": [
            {
                "name": "wp",
                "href": "https://api.w.org/{rel}",
                "templated": true
            }
        ]
    }
},
"post_tag": {
    "name": "Tags",
    "slug": "post_tag",
    "description": "",
    "types": [
        "post"
    ],
    "hierarchical": false,
    "rest_base": "tags",
    "_links": {
        "collection": [
            {
                "href": "https://cms.dboxcg.com/index.php/wp-json/wp/v2/taxonomies"
            }
        ],
        "wp:items": [
            {
                "href": "https://cms.dboxcg.com/index.php/wp-json/wp/v2/tags"
            }
        ],
        "curies": [
            {
                "name": "wp",
                "href": "https://api.w.org/{rel}",
                "templated": true
            }
        ]
    }
},
"dog": {
    "name": "Dogs",
    "slug": "dog",
    "description": "",
    "types": [
        "poodle",
        "labrador",
        "beagle",
        "retriever"
    ],
    "hierarchical": false,
    "rest_base": "dog",
    "_links": {
        "collection": [
            {
                "href": "https://cms.dboxcg.com/index.php/wp-json/wp/v2/taxonomies"
            }
        ],
        "wp:items": [
            {
                "href": "https://cms.dboxcg.com/index.php/wp-json/wp/v2/dog"
            }
        ],
        "curies": [
            {
                "name": "wp",
                "href": "https://api.w.org/{rel}",
                "templated": true
            }
        ]
    }
}

}

I am trying to retrieve the array of dog types in a custom plugin.

[
    "poodle",
    "labrador",
    "beagle",
    "retriever"
]

How do I access the above array via wordpress hooks? I have tried the following with no luck:

get_taxonomy('dog')->types;
$wp_taxonomies['dog']->types;

Here is the code I am trying to implement in a custom plugin:

$dog_types = get_taxonomy('dog')->object_type;

foreach ($dog_types as $type) {
    add_filter( "manage_{$type}_posts_columns", 'update_dog_type_columns' );
    add_action( "manage_{$type}_posts_custom_column", 'update_dog_type_column', 10, 2 );
}

function update_dog_type_columns( $columns ) {
    $columns = array(
        'cb' => $columns['cb'],
        'title' => __( 'Title' ),
        'image' => __( 'Thumbnail' ),
        'date' => __( 'Date' )
    );

    return $columns;
}

function update_dog_type_column( $column, $post_id ) {
    switch ( $column ) {
    case 'image':
        $vimeo_link = get_field('vimeo_link');
        if ($vimeo_link) {
            $vimeo_logo_url = 'https://imageurl/vimeo_logo.jpg';
            echo '<img src="' . $vimeo_logo_url . '" height="100px" width="100px" />';
        break;
        } else {
            $img_array = get_field('image');
            $img = $img_array['sizes']['thumbnail'];
            echo '<img src="' . $img . '" height="100px" width="100px" />';
            break;
        }
    case 'year':
        echo get_field( 'year', $post_id );
        break;
    }
}