Path: /admin-api/posts/sending-a-post
To send a post by email, the newsletter query parameter must be passed when publishing or scheduling the post, containing the newsletter’s slug.
Where to find the newsletter slug should be documented here. I don't see in the admin area. I did find it by using browse dev tools and inspecting the data structure returned from GET /ghost/api/admin/newsletters/?include=count.active_members%2Ccount.posts&limit=50
It seems that the first newsletter always has the slug default-newsletter. That could be worth mentioning.