Does the Chapter of Eights shed light on the Jhanas?

Learn to cook, learn to meditate, and after that return to theory to boost your understanding.

This is presumptuous and condescending. I have meditated for many years. My practice informs my study of the canon.

But first I will note that the chapter of eights contains no direct insight on Jhana, but contains a crucial reference to liberation, which is also important for Jhana.

I have to disagree with you here. I think the references to jhanas are there, but indirect. They can be seen more directly when comparing the texts of the Chapter of Eights with MN119.

In the time of Buddha there was oral tradition, not written. This makes that a specific analogy on vitakka and vicara could not be made.

All we have is the texts. I am comparing early texts. How does the fact that there was an oral tradition prevent analogies between early texts?

Vitakka and vicara can be seen as switching between the actual cooking and the use of the book with recipes
… [I am using ellipses because it is such a large part of your post that someone should just go back to the original.]
This is my understanding on vitakka and vicara.

This appears to me to be an idiosyncratic understanding of vitakka and vicara. Do you have anything to back it up?