Suppose then, than I publish the book explicitly as a replacement for the other book. Not as in "this is the same" but as in "if you find a reference to a chapter in the other book, you can also just look here". Would that be copyright infringement?

What happens if I do this to a technical document (think a 3gppp spec) where the TOC runs for 10 pages for a 300 page document, with headings nested 5 deep?

If this argument is valid, it means that APIs are not copyrightable, they are patentable, because copyright is only for expressions of ideas, not for machines; patents are what apply to machines. And Oracle has already lost on the question of patent infringement in this case (back in 2015, IIRC).

That is incorrect.

> . If I change the names of things in a table of contents to synonyms, I can still use it to find what I am looking for.

If I change the name to be something you cannot refer to, you cannot.

> If I change the names of things my implementation of an API, it no longer functions as an interface for the things that worked with it previously.

This is irrelevant to the API. The API does not make a guarantee about functionality. If I have an endpoint /foo and later /foo increments an internal counter by 1, the API remains unchanged. Documentation supplements and is not part of the API per se, which is an important distinction. The fact that Documentation and an API are being referred to in conjunction, was a failure that software will suffer for more than the lifetime of my children.