Assuming $username is set somewhere you need to use <?php ?> tags to actually echo something:
<?php if(isset($_SESSION['username'])): ?>
<li><a href="https://stackoverflow.com/questions/52586942/logout.php">Logout</a>
<?php echo $username; ?>
</li>
<?php else: ?>
<li><a href="login.php">Login</a></li>
<?php endif; ?>
If $username is not set, use the session var:
<?php if(isset($_SESSION['username'])): ?>
<li><a href="https://stackoverflow.com/questions/52586942/logout.php">Logout</a>
<?php echo $_SESSION['username']; ?>
</li>
<?php else: ?>
<li><a href="login.php">Login</a></li>
<?php endif; ?>
solved PHP swap between login/logout when user login/logout [closed]