Question

in Marian Anderson sings the author begins the story by putting the reader right in the middle of the action what is the term for this type of organization

Answer 1

When you come across the situation where the author begins the story by putting the reader right in the middle of the action it means that he wants to appeal or even interact with a reader, and it is a direct characterization of Second person point of view.
I am sure that helps!

Answer 2

the answer is actually in medias res.

proof: in me·di·as res

/in ˈmēdēəs ˈres,ˈmādēˌäs/Submit

adverb

into the middle of a narrative; without preamble.

"having begun his story in medias res, he then interrupts it"

into the midst of things.