Binding server connect variable inside Javascript

Seeing the php dump I think the session variable you want is $_SESSION["userdata"][0]["email"].

So in your script it would then become

<script type=“text/javascript”>
  var Tawk_API=Tawk_API||{};
  Tawk_API.visitor = {
    name : '<?php echo $_SESSION["userdata"][0]["FirstNames"] ?>',
    email : '<?php echo $_SESSION["userdata"][0]["email"] ?>'
  };
  var Tawk_LoadStart=new Date();
  // rest of the tawk.to widget code 
</script>

App Connect expressions in script blocks will not work, but PHP can be used inside the script blocks.