> It is my understanding that a KDF adds entropy, whereas a hash loses information.

KDFs are hash functions (or families of hash functions, depending on your definition), just ones with a lot of complexity. It is sometimes said that they "add entropy" but that usually means either 1) they combine entropy from a salt into the password hash (which you can do with any hash function) or 2) they make the password more computationally difficult to crack *as if* it had more entropy (also called computational entropy).

Likewise, both KDFs and hashes "lose information" in the sense that collisions usually mean their image is smaller than their [domain][1]. That does not make them stronger, however, since if two passwords give the same output hash, either can be used as authentication.

So using a hash after a KDF is at best redundant and can lead to less security through e.g. increased collisions.

  [1]: https://en.wikipedia.org/wiki/Domain_of_a_function