Your first article still doesn’t hold any usefull information about your installation.
Anyway, I begin to see what your issue is.
First of all:
Agents currently can not be customers of other groups within the UI at the moment. This currently works as designed - however, we’d like to change that in the future.
You can find more information on that topic here, if you’re interested:
Check out the channel “Web” which is responsible for allowing to see your user to see one or more groups to select from. If the customer doesn’t see the group field at all, you might have selected a specific group.
https://admin-docs.zammad.org/en/latest/channels/web.html
You have two options:
Allow your management to view IT tickets if needed or at least allow them to “write” (only that one permission) to the IT group.
This allows your agents to move tickets from group to group which might make a lot of sense if a ticket got routed the wrong way for whatever reason.
More information on permission can be found here:
https://admin-docs.zammad.org/en/latest/manage/users.html#the-assignment-of-rights-permissions
(That part actually is identical to the one in roles and behaves the same way)