Authentication API script
I would make my review mostly on the security, with some other improvements.


The main issue with this code, obviously, is SQL injection. It can easily allow anyone to browse the whole contents of your database. You should be really using prepared statements for the every SQL query you run, if at least one variable is going to be used in it.
Worse yet, by echoing the error out, you ease the task for the attacker significantly. By getting the feedback for their actions through the error message, an attacker could save themselves a lot of time. In case of error, only a generalized error message should be ever sent outside. 
a somewhat similar issue: never give a potential hacker any certain feedback regarding the correctness of login and password - it's none of their business. Whereas a honest user could be just informed that their credentials didn't match. So it should be the only response in case of the wrong credentials.
Another issue is HTTP method used. It is considered a good practice to use POST method for the credentials, as it has a much lower footprint. For example, when using GET method, you will have all user passwords stored in the server's access log in the raw form. Why bother with hashing them in the database, if raw passwords can be easily accessed anyway?


I also removed redundant isset() calls. Given you already tested your input variables with isset, a condition $username = isset($_GET['auth_username']) will never be evaluated to false. So I just removed it altogether.

A note on the error reporting. Like it is said above, a system error message should be never echoed outside. At the same time, it should be logged carefully for the site admin's reference. Seemingly contradicting at first, there rules are  perfectly go together. I wrote an article on the PHP error reporting in which I summarized all my experience and which I highly recommend to read.

So the code would be

&lt;?php

error_reporting(E_ALL);
ini_set('display_errors', 0);
ini_set('log_errors', 1);
mysqli_report(MYSQLI_REPORT_ERROR | MYSQLI_REPORT_STRICT);

try {
    $connection = mysqli_connect("localhost","root","","mydb");

    if (!isset($_POST['auth_username'],$_POST['auth_password'])) {
        exit('you failed to provide the correct parameters.');
    }

    $sql = "SELECT password, has_subscription FROM a__client_accounts WHERE username=?";
    $stmt = $connection-&gt;prepare($sql);
    $stmt-&gt;bind_param("s", $_POST['auth_username'])
    $stmt-&gt;execute();
    $stmt-&gt;store_result();
    $stmt-&gt;bind_result($db_password, $has_subscription);

    if ($stmt-&gt;fetch() &amp;&amp; password_verify($_POST['auth_password'], $db_password)
    {
        if (!$has_subscription)
        {
            exit('you authenticated, but you don\'t have a subscription');
        } else {
            exit('congratulations');
        }
    } else {
        echo 'wrong login or password';
    }
} catch (\Exception $e) {
    error_log($e);
    exit("server error");
}