Send Mail after Form Submit to Google Sheet

I found this wonderful app script on Github for writing to my Google spreadsheet. It works perfectly. Now I'm looking for a way to send myself an email after the script has run. But this is proving difficult. I want to call my own EmailNote() function. It works very well on its own, i.e. when started from the editor, but when I try to integrate it in the doPost(e) script, no email is sent. Kindly ask for help!

My doPost(e) Script:

// Manual: https://github.com/levinunnink/html-form-to-google-sheet

var sheetName = 'Entries' var scriptProp = PropertiesService.getScriptProperties()

function intialSetup () {
  var activeSpreadsheet = SpreadsheetApp.getActiveSpreadsheet()
  scriptProp.setProperty('key', activeSpreadsheet.getId())
}

function doPost (e) {
  var lock = LockService.getScriptLock()
  lock.tryLock(10000)

  try {
    var doc = SpreadsheetApp.openById(scriptProp.getProperty('key'))
    var sheet = doc.getSheetByName(sheetName)

    var headers = sheet.getRange(1, 1, 1, sheet.getLastColumn()).getValues()[0]
    var nextRow = sheet.getLastRow() + 1

    var newRow = headers.map(function(header) {
      return header === 'timestamp' ? new Date() : e.parameter[header]
    })

    sheet.getRange(nextRow, 1, 1, newRow.length).setValues([newRow])
    return ContentService
      .createTextOutput(JSON.stringify({ 'result': 'success', 'row': nextRow }))
      .setMimeType(ContentService.MimeType.JSON)
  }
 
  catch (e) {
    return ContentService
      .createTextOutput(JSON.stringify({ 'result': 'error', 'error': e }))
      .setMimeType(ContentService.MimeType.JSON)
  }

  finally {
    lock.releaseLock()
  }
}

My EmailNote() Script:

function EmailNote() {
  var emailSender = "my.mail@gmail.com";
  var emailRecipients = ["my.mail@gmail.com", "my@mail.com"];
  var emailSubject = "App Script - Email";
  var emailBody ='App Script - Email';

  // send mail
  GmailApp.sendEmail(emailRecipients.join(","), emailSubject, emailBody, {
    from: emailSender
  });
}

Adding another answer as this is something that is a very common pitfall new and often even experienced engineers fall prey to.

Make sure you redeploy your app after making any changes. And after deployment use the updated endpoint.