The Resources module was moved into the Planner module, and it only holds lesson-related resources, so not necessarily what you’re looking for.
Be sure to check out System Admin > Custom Fields, there is a File field type which can be added to the many different areas of the system that support custom fields. There are also Personal Documents which are designed for ID and certificate-style documents, which can also be configured for either students or staff.
The hidden setting may be what you’re looking for. It means that the fields will only show up on the back-end Edit pages for the respective data types, so hidden User fields will only show up in Edit User and not in the profile, same for staff, medical, etc.