With the exception of the fuzzy part, which can be added separately, Bash already has facilities for all of those functionalities.
The "remembering" part can be done via dirs/pushd/popd. The "using the basename only" part can be done via CDPATH. The "automated" remembering could be done via a super simple function wrapper over 'cd', adding things onto the the dirstack or the CDPATH respectively (and with a selection menu, possibly fuzzy, when clashes occur)
Putting it all together to achieve the same effect feels like a very simple 10-liner bash function at best.
Not dissing the author's work or idea, nor is there anything wrong with reinventing the wheel in another language for fun; but if you're going to claim that "z is a better cd" because it bundles all that other functionality for things that are unrelated to cd, and for which there are already pretty decent unix-philosophy-adhereing commands that you could be using effectively already, then if you fail to mention these things in your documentation, it feels a bit ignorant / disingenuous. I would have preferred examples with "without z you'd have to use CDPATH for this, and dirstack for that, and maybe this 5-line wrapper for the menu thing, etc".
Otherwise it feels a bit like saying "grep is a better ed" or something.