Here are some findings:
The feature of custom fields is only available in the so called "Premium Plan" (that's already known from this thread).
ONLY Teams shows the possibility to upgrade to a premium plan (I was able to activate a trial).
A premium plan created in Teams is only visible in Teams. Neither visible in the web app nor in the iOS app.
So far for me it is not possible to add attachments from disk or sharepoint because the two options are greyed out.
The market place in the m365 admin console does not show a premium plan for Planner, the only thing I find when searching for "Planner" is "Planner Plan 1".
So everything together this is not usable at the moment, not buyable and maximum confusing.
Hope this improves soon, becuase the simplicity of the Planner app is really appreciated but it lacks the requirement of having separate fields for important information. If the price is then not reasonable it would be better to change to another software tough more complex definately more flexible (e.g. Jira).