Quick Sort Algorithm (Python)
I'm all for providing docstrings.
I doubt the docstrings presented are helpful as can be for someone not familiar with the quicksort algorithm:


Returns an ascendingly sorted list;
is this a new one or the one provided as input?
(A method docstring should start with a phrase ending in a period [prescribing the] method's effect as a command ("Do this", "Return that"), not as a description)
Input variable is an integer or float array;
doesn't it work for strings?
the python tutorial names lists and tuples as standard sequence data types - what is an array?
(The type hint does give a hint as to the intended meaning - I do not have a helpful intuition about python type hinting in general and "interaction" with docstrings in particular.)
Theoretical Complexity: O(N×Log N) Time and O(N) Memory
Without further qualification of the bounds claimed, I expect them to be worst case bounds.
Recursively sorts the two pivot-divided sublists;
looking at the method interface, only, I don't see two sublists
(which happens to be the first thing I hope for in a method docstring - The docstring for a function or method should summarize its behavior and document its arguments, … does not stress this.)


There are several things not quite pythonic in the code presented


a swap of a and b is typically denoted using implied lists:
a, b = b, a
Concatenating immutable sequences always results in a new object of the same type as both sequences (the type of the first operand if not same types(?)) - not seeing the intention in enclosing test_list_integer + test_list_float in list()


I prefer  

if not &lt;condition&gt;:
    &lt;get out of here&gt;
&lt;operate&gt;


over

if &lt;condition&gt;:
    &lt;operate&gt;
else:
    &lt;get out of here&gt;