OK first of all I want to thank you @all for your help to analyse this.
The good news is that I managed to send campaign emails on my test instance again.
It looks like the template_id column is not used any more. It is still empty.
So @Daman gave the correct hint. After the recreation of my outbound email settings. I gave this another try.
I’m running my outbound email without authentication and the user name value need to be filled to be able to send emails.
So I would say this is a bug.
Beside that I have configured a timezone inside the php.ini and I have deactivated the “Run Nightly Mass Email Campaigns” schedule as suggested by @rsp and @anthony.oak.castro .
So I will try to replicated this to my production system now. → fingers crossed
Should I open a ticket for the username being required on the outbound email settings?