Writing cleaner PHP code to add additional options
General inconsistency
Basically your code is borderline off topic. Although it could work, it is not a working code in the sense a programmer could take it; but rather a set of copy-pasted code blocks loosely (and wrongly) connected to each other.
The main problem is inconsistent code structure. You have $data['success'] set at the end of the script but... it goes nowhere.
So it basically should be
if ($errors) {
    $data['success'] = false;
    $data['errors']  = $errors;
} else {
    $mail = new PHPMailer;
    // the rest or phpmailer code goes on
    if(!$mail-&gt;send())
    {
        $data['success'] = false;
        $data['errors']  =  [&quot;Mailer Error: &quot; . $mail-&gt;ErrorInfo];
    }
    else
    {
        $data['success'] = true;
        $data['message'] = 'Success!';
    }
}
// return all our data to an AJAX call
echo json_encode($data);

Note that another error has been fixed. $data['errors'] should be an array, but in case of phpmailer error you were sending a string.
Configuration options
error_log( &quot;Errors&quot; );

Always use the absolute filesystem path to a log file or you'll end up with log files in the every directory.
Also, it's better to configure such settings on the server level, for some errors may occur before the file gets parsed completely. Or at least put these settings into a configuration file and include it in all your php scripts.
Autoload
Instead of requiring files manually, consider using PSR-4 autoload and Composer. It's really easy, you just have to install Composer, then run two commands in console
php composer.phar require google/recaptcha
php composer.phar require phpmailer/phpmailer

and then add just a single require line into your code
require __DIR__ . '/vendor/autoload.php';

and all classes will be loaded automatically!
Validation and sanitization
You may want to verify whether the email address is valid.
if (empty($_POST['emailAddress'])) {
    $errors['emailAddress'] = 'Email Address is required.';
} else {
    $emailAddress = filter_var($errors['emailAddress'], FILTER_SANITIZE_EMAIL);
    if (!filter_var($emailAddress, FILTER_VALIDATE_EMAIL)) {
        $errors['emailAddress'] = 'Email Address is invalid.';
    }
}

and also sanitize the email body,
$emailBody = htmlspecialchars($_POST['comment']);