You're trying to write code which outputs code which outputs the address. Why? You're already in the context of outputting something from the PHP code:
echo "something...";
If what you want to output is the value of $address then just output that:
echo "<span>$address</span>";
I suspect the reason you did it that way is because you're expecting the currently loaded page to parse and execute that PHP code. This is a fundamental misunderstanding of how these technologies work. The PHP code for that page executed once, on the server, and delivered the resulting HTML/CSS/JavaScript to the client.
The AJAX operation is making a new, separate request to another PHP resource which will execute on the server and output back to the client. In this case it's just outputting a string value, which the client-side JavaScript code will then write to an element on the page:
$("div").text(result);
(This is a good opportunity for you to use your browser's debugging tools and observe the AJAX request/result in the network tab, to see what's actually being sent/received. At no point should actual PHP code be visible to the browser. All of that is executed on the server.)
The reason this is important is because, if this is the case, then you are likely misunderstanding where $address is defined. If it's defined in the PHP script which rendered the page you're looking at, that doesn't mean it's defined in address.php. If the code you're showing us for address.php is the entirety of that page then $address is not defined.
So you'll need to define $address on that page.
After having said all of that... You might find it much easier not to involve AJAX for this at all in the first place. Just output the address to the page but style the <span> to not be visible. Then when the user clicks the button, make it visible. No need for the complexity of an entirely new HTTP request:
$('button').click(function () {
$('span').show();
});
span {
display: none;
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<button>Click</button>
<span>this is the address</span>
$addressinaddress.php?