Jason Hendriks on "[Plugin: Postman SMTP Mailer/Email Log] WordPress (or another plugin) is currently handling email delivery, not Postman."

Look in the Diagnostic Test at WordPress wp_mail Owner. You need to deactivate the plugin which is the other owner. For example:

WordPress wp_mail Owner: /wordpress/wp-content/plugins/sendgrid-email-delivery-simplified/lib/overwrite-sendgrid-methods.php

Sometimes the Owner shows "pluggables.php", this means that a plugin is loading a WordPress core file directly which is wrong and in order to find which one you'll have to deactivate all of them and reactivate one at a time.

See https://wordpress.org/tags/wp_mail-conflict