My team is currently working on an integration of the Mendeley reference platform into our Web-App. We want to display the references of a logged in user in a sidebar.
To provide a familiar look and feel, we structure the data received from API calls like the original Mendeley library page ("All Documents", "Favorites", "My Publication", folders, groups, and subfolders), but we found no way to categorize a document/reference as "Recently Read" and/or "Recently Added".
I'm afraid there is no public API endpoint to provide the list of "Recently Read" documents.
As for "Recently Added" - you can obtain these with the publicly available API. Take a look at https://api.mendeley.com/apidocs/docs#!/documents/getDocuments. You can retrieve a list of documents ordered by their creation time.
Example GET URL for "Recently Added"
https://api.mendeley.com/documents?view=client&sort=created&order=desc&limit=50