How do I create a pop up authorization for my Google Web App

Question

I'm new to Web Scripts and deploying web apps, I have an issue where I require users to authorize permission to use the web app, but nothing pops up to request for said authorization.

I found this post here and it seems to be what I needed but I'm unsure how would I use it. I tried calling onOpen function at the start of my doGet but nothing happens. I also don't see where/when the authorize function is being called. My Web App is also using sheets, so I deleted any lines of code dealing with DocumentApp.

Here is my modified version of the code

function onOpen() {
  if(!UserProperties.getProperty('author')){
    var html = HtmlService.createHtmlOutputFromFile('index1')
    .setTitle("Install Menu").setWidth(400);
  }else{
    var html = HtmlService.createHtmlOutputFromFile('index2')
    .setTitle("Mailmerge Menu").setWidth(400);
  }
}

function authorize(){
  UserProperties.setProperty('author','yes');
  var html = HtmlService.createHtmlOutput('Authorization complete<br>Thanks<br><br>please refresh your browser').setTitle("Confirmation").setWidth(400);
}

This is my doGet function just in case I was not utilizing the functions correctly.

function doGet(e)
{
  onOpen();

  var result;
  
  var sheets = SpreadsheetApp.getActiveSheet();
  var values = [];

  // Get row 1 data
  for( var i = 3; i <= 16; ++i)
  {    
    var char = String.fromCharCode('A'.charCodeAt() + i) // Increment char
    values.push(sheets.getRange(char + 1).getValue());
  }

  // Get row 2 data
  for( var i = 3; i <= 16; ++i)
  {    
    var char = String.fromCharCode('A'.charCodeAt() + i) // Increment char
    values.push(sheets.getRange(char + 2).getValue());
  }
  
  var result = {result:values};


  var JsonValue = JSON.stringify(result);
  
  return ContentService.createTextOutput(JsonValue.toString()).setMimeType(ContentService.MimeType.JSON);
}

I know I can set the web app to execute as me by anyone, which does work, but I would like be able to allow other users to authorize themselves to execute the app.

Edit: I'm using Unity's WebRequest class to call the Get from my web app.

_webRequest = UnityWebRequest.Get("web app url here");
_webRequest.SendWebRequest();

And on receiving the response I will parse it and use the data in "result" in a separate class

if (_webRequest != null && _webRequest.isDone)
{
    result = JsonUtility.FromJson<WebResponsePacket> 
    (_webRequest.downloadHandler.text);
     Debug.Log("Successful Request");

    return true;
}