Google Recaptcha implementation

Im struggeling to enter the private key for reCaptcha v3. I have integrated in the Site-key into my html form:

<div id="recaptcha" class="g-recaptcha" data-sitekey="SITE KEY" data-callback="onSubmit" data-size="invisible"></div>

Now Im struggeling to enter the private key. I have a file called recaptchalib.php

Will it work if i enter the secret key like this:

class ReCaptchaResponse
{
    public $success;
    public $errorCodes;
}

class ReCaptcha
{
    private static $_signupUrl = "https://www.google.com/recaptcha/admin";
    private static $_siteVerifyUrl =
        "https://www.google.com/recaptcha/api/siteverify?";
    private $_secret ="INSERT SECRET KEY HERE";
    private static $_version = "php_1.0";

    /**
     * Constructor.
     *
     * @param string $secret shared secret between site and ReCAPTCHA server.
     */
    function ReCaptcha($secret)
    {
        if ($secret == null || $secret == "") {
            die("To use reCAPTCHA you must get an API key from <a href='"
                . self::$_signupUrl . "'>" . self::$_signupUrl . "</a>");
        }
        $this->_secret=$secret;
    }

source https://stackoverflow.com/questions/70037333/google-recaptcha-implementation