your button at <figcaption>
its blocked by
<a class="carousel-control-prev" href="#mainBanner" role="button" data-slide="prev">
<span class="prev">«</span>
</a>
<a class="carousel-control-next" href="#mainBanner" role="button" data-slide="next">
<span class="next">»</span>
</a>
setting the <figcaption>
position and give z-index
at style like this
css
figcaption
{
position: relative;
z-index: 2;
}
full code
<!DOCTYPE html>
<html>
<head>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/css/bootstrap.min.css" integrity="sha384-TX8t27EcRE3e/ihU7zmQxVncDAy5uIKz4rEkgIXeMed4M0jlfIDPvg6uqKI2xXr2" crossorigin="anonymous">
</head>
<body>
<style type="text/css">
figcaption{
position: relative;
z-index: 2;
}
</style>
<h1><strong>Upcoming Productions</strong></h1>
<div id="banner" style="width: 100%" class="bg-secondary">
<div id="mainBanner" class="carousel slide" data-ride="carousel" data-interval="7000">
<!-- Indicators -->
<ol class="carousel-indicators">
<li data-target="#myCarousel" data-slide-to="0" class="active"></li>
<li data-target="#myCarousel" data-slide-to="1"></li>
</ol>
<div class="carousel-inner">
<!-- Slideshow feature 1 - Production Banner 1
photo banner's dimensions should follow 1100px x 400px -->
<div class="carousel-item active" style="height: 400px">
<section class="showcasecontent"></section>
<figcaption>
<a href="oedipus.php"><div class="productioncontent">
<h2>Oedipus</h2>
<h4>5 - 7 Feb 2021</h4>
<a href="../oedipus.php" class="btn">
Find Out More <i class="fas fa-chevron-right"></i>
</a>
</div></a>
</figcaption>
<br>
</div>
<!-- slideshow feature 2 - Production banner 2
photo banner's dimensions should follow 1100px x 400px -->
<div class="carousel-item" style="height: 400px">
<section class="showcasecontent2"></section>
<figcaption>
<div class="productioncontent">
<h2>Is That It?</h2>
<h4>To be released soon</h4>
<a href="../isthatit.php" class="btn">
Find Out More <i class="fas fa-chevron-right"></i>
</a>
</div>
</figcaption>
<br>
</div>
<!-- Left right controls -->
<a class="carousel-control-prev" href="#mainBanner" role="button" data-slide="prev">
<span class="prev">«</span>
</a>
<a class="carousel-control-next" href="#mainBanner" role="button" data-slide="next">
<span class="next">»</span>
</a>
</body>
<script src="https://code.jquery.com/jquery-3.5.1.slim.min.js" integrity="sha384-DfXdz2htPH0lsSSs5nCTpuj/zy4C+OGpamoFVy38MVBnE+IbbVYUew+OrCXaRkfj" crossorigin="anonymous"></script>
<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/js/bootstrap.bundle.min.js" integrity="sha384-ho+j7jyWK8fNQe+A12Hb8AhRq26LrZ/JpcUGGOn+Y7RsweNrtN/tE3MoK7ZeZDyx" crossorigin="anonymous"></script>
</html>