Having browsed the official WordPress REST API site - and looking at the various endpoints - I cannot find information of custom post types. I appreciate there is the WordPress REST API Plugin that appears to add support for CPT's - but does the official API support them?
If not - is there a reason for this?
I got the same doubt about Wordpress Rest API and I also read the Wordpress rest API docs. If you want to create custom post type using Rest API then you can use this plugin Wordpress JSON API. In this plugin you just need to create function in controller folder ( posts.php ) make sure your auth should be on, for that you can use json-api-user.