Turns out I was not yet as happy as I could be. 
Yes, I can see the ticket text. I can open and close the ticket via the “status” widget.
But there does not seem to be any context around the ticket. Like organization.
The field widgets that I usually see and not with this ticket are: Group, Owner, Priority, Labels, Linked to, Time units.
Looks like the tickets appear in the ‘unassigned and open’ list of tickets. I am the admin but can not assign the ticket to somebody (me).
Adding some columns to this view I see that these tickets have no owner. Sure, but how to assign them to somebody?
Ah, ok. These tickets have been assigned to the group ‘users’ and I have disabled the group ‘users’ because I use 2 other groups for my internal workload. So enabling the group ‘users’ and add ign full rights to this group to user me.
Yes, now I see al created tickets and can reassign.
Next step is figuring out how I can use the API to assign created tickets to another group.
Duh! It’s right there in the docs: “group”: “Users”.
Okay, so it’s hard coded in the Zabbix javascript for this Zabbix media type.
This won’t do. Making it configurable.
Closing this article.