and it was in the first 2 results

if you check in the Chrome console you'll notice this error:

Uncaught ReferenceError: jQuery is not defined

this is because your code is trying to use jQuery ... but you are not importing jquery on the page!
as explained by your third part: <!-- bookingWidget requires jQuery and jQueryUI -->

so to fix it, you must import jquery FIRST!

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.min.js" integrity="sha256-9/aliU8dGd2tb6OSsuzixeV4y/faTqgFtohetphbbj0=" crossorigin="anonymous"></script>

So the final code that you should place in the block of HTML source code will look like this:

<!-- bookingWidget requires jQuery and jQueryUI -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.min.js" integrity="sha256-9/aliU8dGd2tb6OSsuzixeV4y/faTqgFtohetphbbj0=" crossorigin="anonymous"></script>

<!-- Include the following line ONCE ONLY on the page, preferably in the document head -->
<script src='https://media.xmlcal.com/widget/1.00/js/bookWidget.min.js'></script>

<!-- Place this div on your page where you want the widget to show -->
<div id='bookWidget-62596-111720-0-1589445879'> </div>

<!-- The following will initialize the widget in the above div -->
<script>
jQuery(document).ready(function() {
jQuery('#bookWidget-62596-111720-0-1589445879').bookWidget({
propid:111720,
formAction:'https://www.beds24.com/booking.php',
widgetLang:'en',
widgetType:'BookingBox'
});
});
</script>