Hi Rick,
Thanks for choosing Microsoft.
May I confirm do you mean let the students upload their work to class notebook in Teams? If so, as we all know OneNote class notebook has three-types of sub-notebooks, including Student Notebooks, Content Library and Collaboration Space. Please check this
article for more information:
Getting Started with the OneNote
Class Notebook: A Walkthrough for Teachers

As for your requirement, I think the students themselves can upload their work in their notebooks via clicking Insert>File> Insert as Attachment, and only teachers and students themselves can see their own work, not for all students.
In addition, I think you can also try to create an assignment in Teams to let them upload their files to you. Please go to your class team> click Assignments tab> Create> Assignment> follow the steps> click Assign> then the students can upload their work
to you.
For more details, please refer: Create an assignment in Microsoft Teams

If this is not what you mean, please point out and we will further investigate it.
We are glad to help, you can post back at your convenience.
Best regards,
Gloria