The C in CPS and the cc in call/cc are exactly the same thing.

It’s a continuation. You don’t need to express your program in continuation passing style to use continuation which is why call/cc exists.

The idea of continuation is interesting in and of itself independently of if your compiler uses CPS because continuation as a concept is useful. It appears in effect system for exemple.

Apple book is very good by the way. It gives a very hand on overview of how to implement a compiler in a functional style and neatly introduces some quite complex ideas. To me it’s amongst the books you can’t regret reading also it’s quite short and easy which helps. Timeless classic like Peyton Jones The implementation of functional programming languages and is great introduction to lambda calculus and presentation of how to implement a type checker in Miranda.

It might be a cool book but it describes an outdated way to write compilers, even if you’re writing compilers for functional languages

What does that mean?

The book introduces how to turn a program to CPS, why you can and how that allows to compile. That’s interesting in and of itself as a way to conceptualise how a program computation flows work and what it means for the construction of functional programs.

It was never a popular way to write compilers but academic books are not tutorial. That never was the point.