Hello Jennifer,
From your description I understand that you want to be able to move folders in Teams app. However, by my test I think currently this feature might be not feasible in Teams. As a workaround,
you may try to open it in SharePoint site:
And then click “Show actions” icon->Move To and check if this way meet your requirement:
If there’s any problem, please feel free to contact me.
Best Regards,
Anna