I am building an app to create / update paper docs by selecting a dropdown containing a list of folders and papers in a tree structure. Which API or combination of APIs can I use to retrieve all the folders and list of papers inside each folder.
Dropbox doesn't offer a way to list Paper folders and docs exactly like that. You'll need to use /2/paper/docs/list and /2/paper/docs/list/continue to list docs themselves, and then use /2/paper/docs/get_folder_info to get the folder info. You can then use that information to create the structure you want.
