shared app directory, exists but inaccessible to my app

When you say you created an app with "limited access", I presume you mean you registered an app with the app folder permission. When calling /sharing/list_shared_links with an app folder app, and not specifying a path parameter, it will only return shared links that exist for files that has access to, i.e., in its app folder.

The output you shared, with an empty links array, would be expected if there aren't any shared links created for files in that app folder. Is that the case? (The true has_more value is known issue though.)

If you just want to list the contents of the app folder, regardless of shared links, you can use the /files/list_folder endpoint:

https://www.dropbox.com/developers/documentation/http/documentation#files-list_folder