I used the previous version of Groove before MSFT aquired it for $82M.
It's a nice system. I wish the groove workspace could be backwards compatible.
The best part is having the chat system and the project management system linked together. So if you are chatting with somebody, then you know that the tasks can be viewed at the same time.
There are a few open source projects that do project management, but not with integrated chat and whiteboard like groove.
Depending on your access rights, you should be able to create, rename, and move folders in the file tab.