Is setting $mail->SMTPDebug = 0; sufficient to suppress error messages in PHPMailer, or are there other methods to achieve this?

To suppress error messages in PHPMailer, setting $mail->SMTPDebug = 0; is sufficient. This will disable debugging output, including error messages. Additionally, you can also set the $mail->Debugoutput property to 'error_log' to log errors to the PHP error log.

$mail->SMTPDebug = 0;
$mail->Debugoutput = 'error_log';