While you can copy a set of folders in the Documents tool from one project to another, any files within those folders are not included. See Can I copy one project's Documents folders to a new project?
Yes. However, the only files that can be copied over are files that exist in the project's root folder (see arrow in the image below).
To check to see what files can be copied over, click the project's root folder at the top of the document structure and look for files that are shown outside of the folders (see outlined portion of image below). As long as the root folder is selected when you upload or move documents, the files will be included when you copy a folder structure to another project.