A wrapper for user authentication using cURL in PHP
Let me be frank: this code is just a Frankenstein sewn from different unrelated parts. Basically here are two main problems:

sending HTTP requests is a distinct task and should be performed by another wrapper
splitting the main functionality between two methods just makes no sense. I do understand that you probably wanted to make use of constructor, but that's not how it is done

The HTTP request class
Basically there must be a class that does HTTP requests with methods to set particular settings, such as

setAuth(new BearerAuth($token))
setContentType()
setUrl()
etc

The error checking
Also, in this class, it is important to check for errors. Right now your code returns whatever is sent by the other party. But it is not necessarily would be JSON of a particular format. It could be HTML, JSON that contains some different data, an empty string, etc.

First of all the code must check for the curl_error. In case there is, it must throw an Exception
Then it must try to decode JSON. If it fails it must throw an Exception
Then it must check if the decoded data contains expected information. If it doesn't,  it must throw an Exception
only then it must return the data

The actual class
And then there could be a class to interact with a particular API, something like this
class Nucleolus
{
    protected $transport;
    protected $host;

    public function __construct(string $host, string $token)
    {
        $this-&gt;transport = new HTTPTransport;
        $this-&gt;transport-&gt;setAuth(new BearerAuth($token));
        $this-&gt;transport-&gt;setContentType('application/json');
    }

    public function authenticate(string $username, string $password, string $serverUrl = null)
    {
        $this-&gt;transport-&gt;setUrl($this-&gt;host.&quot;/authen/user&quot;);
        $result = $this-&gt;transport-&gt;post([
            'url' =&gt; $serverUrl ? $serverUrl : $_SERVER['SERVER_NAME'], 
            'username' =&gt; $username, 
            'password' =&gt; $password,
        ]);
        $data = JSON::decode($result);
        if ($data === true)
            return true;
        } else {
            throw new NucleolusException(&quot;Incorrect data from auth: $result&quot;);
        }
    }
}

Destructor is not really needed as PHP will destruct everything itself.