The above answer are all wrong. I have watched your video, and the reason behine is your code is using bootstrap-4, instead of bootstrap-5.
I have tested your code with bootstrap-4 starter template, and now it works.
<!doctype html>
<html lang="en">
<head>
<!-- Required meta tags -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
<!-- Bootstrap CSS -->
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/css/bootstrap.min.css" integrity="sha384-zCbKRCUGaJDkqS1kPbPd7TveP5iyJE0EjAuZQTgFLD2ylzuqKfdKlfG/eSrtxUkn" crossorigin="anonymous">
<title>Hello, world!</title>
</head>
<body>
<li class="nav-item dropdown show">
<a class="dropdown-toggle nav-link text-dark" href="#" data-toggle="dropdown">Admin</a>
<div class="dropdown-menu">
<a class="dropdown-item">Categories</a>
<a class="dropdown-item">Media Types</a>
</div>
</li>
<!-- Optional JavaScript; choose one of the two! -->
<!-- Option 1: jQuery and Bootstrap Bundle (includes Popper) -->
<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/jquery.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-fQybjgWLrvvRgtW6bFlB7jaZrFsaBXjsOMm/tB9LTS58ONXgqbR9W8oWht/amnpF" crossorigin="anonymous"></script>
<!-- Option 2: Separate Popper and Bootstrap JS -->
<!--
<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/jquery.slim.min.js" integrity="sha384-DfXdz2htPH0lsSSs5nCTpuj/zy4C+OGpamoFVy38MVBnE+IbbVYUew+OrCXaRkfj" crossorigin="anonymous"></script>
<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/umd/popper.min.js" integrity="sha384-9/reFTGAW83EW2RDu2S0VKaIzap3H66lZH81PoYlFhbGU+6BZp6G7niu735Sk7lN" crossorigin="anonymous"></script>
<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/js/bootstrap.min.js" integrity="sha384-VHvPCCyXqtD5DqJeNxl2dtTyhF78xXNXdkwX1CZeRusQfRKp+tA7hAShOK/B/fQ2" crossorigin="anonymous"></script>
-->
</body>
</html>
Check the starter template by here.
If you sure your whole ASP.NET Core MVC Bootstrap's version is 5.1, your code won't work.