I am not sure why if you trigger the function, nothing happens

loginButton.addEventListener("click", function() {
  const password = document.getElementById("password").value;

  if (password === "password") {
    alert("Correct!");
    document.innerHTML = <embed src="http://stackoverflow.com" style="width:500px; height: 700px;"></embed>;
  } else {
    loginMessage.textContent = "Invalid password.";
  }
});

I was expecting a embed of a website

>Solution :

There are at least four separate reasons your code doesn’t work.

document doesn’t support innerHTML

innerHTML is a property found on HTML elements. The document object is not an HTML element.

Consider document.body.innerHTML instead.

innerHTML expects a string

As pointed out by Mina, <embed src="http://stackoverflow.com" style="width:500px; height: 700px;"></embed> is a syntax error in JavaScript.

You should see this error reported in the Console of your browser’s developer tools.

You need to assign a string to innerHTML. Wrap the code in ' (or " and escape the " in the data).

= '<embed src="http://stackoverflow.com" style="width:500px; height: 700px;"></embed>';

<embed> isn’t for HTML documents

Also note that according to MDN:

Keep in mind that most modern browsers have deprecated and removed support for browser plug-ins, so relying upon <embed> is generally not wise if you want your site to be operable on the average user’s browser.

Consider <iframe> instead.

Stackoverflow forbids it

Stackoverflow has a CSP that forbids other sites from embedding it.