The old getDelta() returns everything for an "App Folder", meaning the app folder and all its subfolders.
It appears that the new listFolder/Continue() isn't really equivalent in that way. It seems to list the files and if you want subfolders you need to make another listFolder call to delve deeper. I can figure out if those paths are absolute or relative, but I'm unclear on how to handle the cursors for the subfolders. Can I just keep track of the app folder one, or do I need to track subfolder cursors as well?
The equivalent of v1's getDelta on v2 is listFolder with recursive=true and listFolderContinue.
Note that both getDelta and listFolder/Continue are paginated, so for both it's possible that the initial call won't contain all of the results. In either case, for a correct implementation you need to save the cursor from the last call and keep calling back (i.e., to getDelta or listFolderContinue) if the previous reply included hasMore=true. You don't need to keep track of multiple cursors. As long as you originally set recursive=true you'll get all entries back.
The documentation for /1/delta and /2/files/list_folder and/2/files/list_folder/continue have more information: