Revealing module pattern modified for more class-like behavior
Review

This is a code review so I will point out some style problems first

Function expressions V statements

There are several ways to ways you can declare a named function. 


As a statement.  function functionName() { }
As an expression. const functionName = function() { };  Note the semicolon


The most important difference between the two is that function statements are hoisted and available in all part of the scope they are declared in. Function expressions are not, even if you declare them as a var (which is hoisted) it remains undefined until it is assigned a value.

Function declared as statements are thus the safest form of function declaration and should be preferred over expression declarations.

testA(); // no error and calls testA
testB(); // throws an error ReferenceError: testB is not defined
testC(); // throws and error TypeError: testC is not a function

function testA(){};
const testB = function(){};
var testC = function(){}; 


const, var and let

When declaring variables use the appropriate type. const is the preferred type, unless you need to modify the value then use var. If you wish to use let in preference to var that is up to you, but be warned that let is not hoisted.

Avoid reserved words.

There is a set of words that are reserved and represent existing, or possible future tokens. Two of these are public, and private you should avoid using reserved words.

There are also many context specific words that you should try to avoid unless you are sure you are not overwriting an existing global property. For example parent, though you safely use it, I do not know if that is just luck or  knowledge that parent is a global scope object AKA window.parent and you are in function scope thus not overwriting the global.

Anti pattern

I consider this as an anti pattern


var Extended = function({extraText = 'no extra text given'} = {}) {
   var parent = Module(arguments[0]);



I am not sure if you are aware that if you call

 Extended(); // without an argument


Then arguments[0] is undefined, and arguments.length === 0 but the destructured argument named extraText has the value "no extra text given"

If you did this in purpose may I suggest that you use an alternative...

const Extended = function(info = {}) {         
    const parent = Module(info);
    info = {extraText : "no extra text given", ...info};


...as it is much clearer what the intent is.        

Use quotes not apostrophes

To avoid confusion with template string declarations delimited by Back Quote try to avoid using Apostrophes (AKA single quite)

Don't duplicate variables

The object Module creates the object private and assign the property text the value of the argument text. This is just a duplication as the only place you use text is in the function it is available as the argument

Design

You are on the correct path to using JavaScript to create private (protected) and public states. Though there is no need to create the private objects as you can use the function scope to hold the private state, including functions

Simple example of a object with both public and private states, using getters and setters to protect type (count as a Number), and access to private state from private and public scopes (eg function 'show')

function MyObj(text = "Nothing to see here."){

     if (typeof text !== "string") {  text = "Wrong type." }

     // private variables
     var count = 0;  // Type safe from outside

     // private functions declared here or in the API below
     function show(){
         console.log(text);
         count += 1;
     }

     // public API also accessible from private scope
     const API = {
         get count() { return count  },
         set count(c) {  // only set if a number to keep type safe state
             if (!isNaN(c)) { count = Number(c) }
         }
         show,  // public access to private function

        // OR add the function here
         show() {
            console.log(text);  // still have private access
            count += 1;
         }
     }

     // internal access 
     setTimeout(show, 1000); // via private function

     // or via public API
     setTimeout(API.show, 2000); 


     return API;
}


You can nest these objects creating additional levels of state security. You can also create several public objects that share a single private state,

A rewrite

As your code does nothing with its private states there was not much to go by. The Design section above would be more appropriate for what you may be after.

The following does the same as your code with considerably less noise.

function Module({text = 'no text given'} = {}) {
    function logText() { console.log(text) };  // private function 
    return { logText };
}

function Extended(info = {}) {
    info = {extraText : "no extra text given", ...info};
    function alertText() { alert(info.extraText) }
    return { ...Module(info), alertText };
}