LibWeb: Only wait for document to be ready for scripts if executing one

HTML fragments are parsed with a temporary HTML document that never has
its flag set to say that it is ready to have scripts executed. For these
fragments, in the HTMLParser, these scripts are prepared, but
execute_script is never called on them.

This results in the HTMLParser waiting forever on the document to be
ready to have scripts executed.

To fix this, only wait for the document to be ready if we are definitely
going to execute a script.

This fixes a hang processing the HTML in the attached test, as seen on:
https://github.com/SerenityOS/serenity

Fixes: #22735

Tests/LibWeb/Text/input/HTML/set-innerHTML-with-script.html

@@ -0,0 +1,9 @@
+<script src="../include.js"></script>
+<div id=container></div>
+<script type="text/javascript">
+    test(() => {
+        let container = document.getElementById("container");
+        container.innerHTML = '<script><\/script>';
+        println("PASS");
+    });
+</script>