While I did not find the solution to my problem, I found the location where my app data can be cleared (which is my main concern). From Google Drive, go to Settings > Manage Apps > Find your listed app. From there, under "OPTIONS", you can "Delete hidden app data".

For the moment, this will be sufficient.

The behaviour I was looking for from WhatsApp seems to be implemented with a different mechanism that still awaits to be discovered. In Storage Manager, WhatsApp backup data is stored under "Clean up other items", while my app data appears to be included with "Google Drive". I'm still not sure what WhatsApp is doing, but it seems to go beyond the standard implementation for Google Drive API.