How to get a post’s associated taxonomies and terms in wp api v2

Ok, I just stumbled upon the answer buried deep in the github issues page:

https://github.com/WP-API/WP-API/issues/1403

The answer is:

the reason is that the terms / meta etc are different objects, and in
typical REST design going a GET on a single resource, will give you
that resource, not that resource and a bunch of other ones too.
However, you can pass _embed to the request which will include the
linked resources in the response, for example see
http://demo.wp-api.org/wp-json/wp/v2/posts/111?_embed