mysqli_select_db() expects parameter 1 to be mysqli, string given

// 2. Select a database to use 
$db_select = mysqli_select_db($connection, DB_NAME);
if (!$db_select) {
    die("Database selection failed: " . mysqli_error($connection));
}

You got the order of the arguments to mysqli_select_db() backwards. And mysqli_error() requires you to provide a connection argument. mysqli_XXX is not like mysql_XXX, these arguments are no longer optional.

Note also that with mysqli you can specify the DB in mysqli_connect():

$connection = mysqli_connect(DB_SERVER, DB_USER, DB_PASS, DB_NAME);
if (!$connection) {
  die("Database connection failed: " . mysqli_connect_error();
}

You must use mysqli_connect_error(), not mysqli_error(), to get the error from mysqli_connect(), since the latter requires you to supply a valid connection.

Your arguments are in the wrong order. The connection comes first according to the docs

<?php
require("constants.php");

// 1. Create a database connection
$connection = mysqli_connect(DB_SERVER,DB_USER,DB_PASS);

if (!$connection) {
    error_log("Failed to connect to MySQL: " . mysqli_error($connection));
    die('Internal server error');
}

// 2. Select a database to use 
$db_select = mysqli_select_db($connection, DB_NAME);
if (!$db_select) {
    error_log("Database selection failed: " . mysqli_error($connection));
    die('Internal server error');
}

?>