How to go through a shared folder and move some of them to a new folder within the shared folder

To list the contents of a folder, you should use /2/files/list_folder[/continue]. You can use that to list the contents of a folder in the connected account, or to list the contents of a folder for which you have a shared link (by setting the 'shared_link' parameter on the /2/files/list_folder call).

To move files from one location to another inside the connected account, you should use /2/files/move_v2. Note that you can't modify or move the contents of a folder if you only have a shared link for the folder, and not access to the folder itself.

To download files from the connected account, you should use /2/files/download. To download files from a shared link, you should use /2/sharing/get_shared_link_file.

By the way, those are links to the documentation for the HTTPS endpoints themselves, but we recommend using one of the official SDKs if possible. Those have corresponding native methods for the HTTPS endpoints.