Example of how you can add the returns from wp_mail_error logs to the EE messages error output

tw_hacky_wp_mail_error.php

<?php // Please do not include the opening PHP tag if you already have one.

add_filter('FHEE__EE_Email_messenger___headers', 'tw_ee_hacky_wp_mail_error_for_messages__EE_Email_messenger___headers', 10, 3);
function tw_ee_hacky_wp_mail_error_for_messages__EE_Email_messenger___headers( $headers, $incoming_message_type, $messenger ){
    add_action('wp_mail_failed', 'tw_log_wp_mail_errors', 10, 1);
    return $headers;
}

function tw_log_wp_mail_errors($wp_error)
{
  $wp_mail_errors = implode(",<br />", $wp_error->get_error_messages());
	EE_Error::add_error(
		sprintf(
			esc_html__(
				'Errors received from wp_mail_failed hook:%1$s%2$s',
				'event_espresso'
			),
            '<br />',
			$wp_mail_errors
		),
		__FILE__,
		__FUNCTION__,
		__LINE__
	);
}