Okay, @Bryan0, @markstos, I think I got it sorted.
This config seems to work.
"mail": {
"from": "<email>",
"transport": "SMTP",
"options": {
"host": "smtp.eu.mailgun.org",
"port": 587,
"service": "Mailgun",
"secure": false,
"requireTLS": true,
"auth": {
"user": "<email>",
"pass": "<password>"
}
}
},