Replace String with value `$&’ not working in javascript

I have string show {{value}} and I want replace {{value}} with $& but it not work. It return current value show {{value}}.
Here is my code

<!DOCTYPE html>
<html>
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<script>
$(document).ready(function(){
  let data ="show {{value}}";
  let output = data.replace("{{value}}","$&");
  alert(output);
});
</script>
</head>
<body>


</body>
</html>

I don’t know why it not work. I try replace with other strings same $1, $a and it work.
How I can fix my problem