First of all, you need to understand the difference between a redirect and a rewrite.

A redirect is a client-side request to have the web browser go to another URL. This means that the URL that you see in the browser will update to the new URL.

A rewrite is a server-side rewrite of the URL before it’s fully processed by IIS. This will not change what you see in the browser because the changes are hidden from the user.

So set your action to rewrite in IIS as shown in the picture below