Z-Function and unique substrings: broken algorithm parroted everywhere?

Question

I am not a huge math nerd so I may easily be missing something, but let's take the algorithm from https://cp-algorithms.com/string/z-function.html and try to apply it to, say, string baz. This string definitely has a substring set of 'b','a','z', 'ba', 'az', 'baz'.

Let's see how z function works (at leas how I understand it):

1. we take an empty string and add 'b' to it. By definition of the algo z[0] = 0 since it's undefined for size 1;
2. we take 'b' and add 'a' to it, invert the string, we have 'ab'... now we calculate z-function... and it produces {0, 0}. First element is "undefined" as is supposed, second element should be defined as:

i-th element is equal to the greatest number of characters starting from the position i that coincide with the first characters of s.

so, at i = 1 we have 'b', our string starts with a, 'b' doesn't coincide with 'a' so of course z[i=1]=0. And this will be repeated for the whole word. In the end we are left with z-array of all zeroes that doesn't tell us anything despite the string having 6 substrings.

Am I missing something? There are tons of websites recommending z function for count of distinct substrings but it... doesn't work? Am I misunderstanding the meaning of distinct here?

See test case: https://pastebin.com/mFDrSvtm