501 5.5.4 このアドレスからの送信は許可されていません

It (probably) means thunderbird is sending from an address like user@example.com and your forum is sending from user@forum.example.com. You may want to change your notification_email address.

Is whatever service that is designed for sending transactional email?

See Troubleshoot email on a new Discourse install

「いいね!」 1