Display post taxonomy REST API

Playing around with VUEJS and the WordPress Rest API I can display my custom posttype on the page. The custom posttype also has a custom taxonomy, but I can’t seem to find a way to display that.
I did read some stuff about adding /?_embed to the endpoint url and ‘show_in_rest => true’ to add support to the API and if I log the result I do get _embedded as an array.
Only the name of the taxonomy isn’t there.

Am I missing some steps to add the taxonomy of the custom post in the API result?

DOM snippet

<div id="workfeed" class="work" style="margin-top: 100px;">
			<div v-for="(item,index) in work" class="row work__item" :data-index="index">
				<div class="col work__item-image">
					<img :src="item._embedded['wp:featuredmedia'][0].source_url" />
				</div>

				<div class="col work__item-content">
					<h3>{{ item.title.rendered }}</h3>
					{{ item.content.rendered }}
					{{ item._embedded['wp:term'].rendered }}
				</div>
			</div>
		</div>

Snippet custom posttype

$args = array(
		'labels'		=> $labels,
		'description'	=> 'All projects',
		'public'		=> true,
		'menu_icon'		=> 'dashicons-layout',
		'supports'		=> array('title', 'editor', 'thumbnail'),
		'has_archive'	=> true,
		'show_in_rest'	=> true,
		'rest_base'		=> 'work-api',
		'rest_controller_class'	=> 'WP_REST_Posts_Controller'
	);
	
	register_post_type('work', $args);
}
add_action('init', 'cptWork', 0);

Snippet custom taxonomy

register_taxonomy('types',array('work'), array(
    'hierarchical' 		=> true,
    'labels' 			=> $labels,
    'show_ui' 			=> true,
    'show_admin_column' => true,
    'query_var' 		=> true,
    'rewrite' 			=> array( 'slug' => 'type' ),
    'show_in_rest'		=> true,
    'rest_base'			=> 'work-api',
    'rest_controller_class'	=> 'WP_REST_Terms_Controller'
  ));
}
add_action( 'init', 'taxWork', 0 );