Hi CDanzmann,
Thanks for exploring Azure Application Insights.
Can you please “Add role assignment” and provide a role of “Application Insights Component Contributor” for your users and see if that helps.

Also you can verify if you can share the existing Workbooks or UserFlows and see if they can view, edit and save them.
One thing I have come across for the UserFlows when you click the +New nothing seems to happen right away , however please click on the edit and save it as a new UserFlow.
Hope the above information helps. If you still see the issue persists please reach out.