idiom = The cat got let out the bag.......... a secret was heard

yes. set out means made formal plans to be followed.....let out means he told when he didn't mean to.

This is not how I have heard the terms used. You MAY say things that are not said often and still have correct sentences. But if you want to say things in a common way, I suggest leaving these phrases to cats in bags and secrets. They are used in this situations. I will find a more common phrase for your sentences.... He has finally announced / made it official / disclosed that he is going away. He has thoroughly explained why / laid out reasons that / charted the causes that has lead to (him / he is) going away.

You let out a secret. You set out plans. He set out plans to go away. Your sentence was wrong.

I was able to understand the meanings of both sentences, and I think both are correct. But neither seems very idiomatic to me. To express these two meanings, I would say: He has announced that he is going away. OR He has let people know that he is going away. He has made it clear that he is going away. OR He has stated specifically that he is going away. An idiomatic example of the use of "set out" might be: I talked to my employee and set out the conditions under which he could keep from being fired.