Custom wordpress taxonomy with v2 api and vue - vue.js

Question

I'm using the wordpress v2 api to display custom posttypes. Everything works as expected, only the custom taxonomy returns their ID instead of the name.
I've read that adding ?embed to the endpoint and show_in_rest adds posttypes and taxonomies to the api result and this sort of looks to be the case. But the taxonomy name isn't found in the result.
Am I missing something?
Here are some snippets of my code...
// taxonomy snippet
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'
// custom posttype snippet
$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'
);
// DOM snippet
<div id="workfeed" class="work" style="margin-top: 100px;">
<div v-for="(item,index) in work" class="row" :data-index="index">
<div class="col">
<img :src="item._embedded['wp:featuredmedia'][0].source_url" />
</div>
<div class="col">
<h3>{{ item.title.rendered }}</h3>
{{ item.content.rendered }}
{{ item._embedded['wp:term'][0].taxonomy }}
</div>
</div>
</div>