I have a number of Document Sets within a Document Library. Is it possible to prevent folders from being created with the "+New" button in the ("root" of the) Document Library itself, while simultaneously allowing folders to be created with the "+New" button within the Document Sets?
Yes, in theory this is possible. Though people have a tendency to find ways around restrictions! I'll explain.
In your document library - check the content types, you'll want to have a Document Set and Document content type. In the Document Library Advanced Settings do not allow folders to be created. Even with these settings, if users use the 'open with explorer' functionality they are no longer restricted in not creating folders! To try and deter this behaviour you can create a new folder yourself and call it "01 - Please do not create folders in this document library!" - people using Explorer might be deterred in this way.
Next, click on your Document Set content type (mine is called Fixture) and then select
Document Set Settings.
In the picture below, see the section titled
Default Content. In my content type, documents are automatically permitted.
If you wish to allow
Folders to be used here, you'll need to create and then add a new
Folder content type. You can create a new
Folder content type at the site level, then go to your Document Library and add the content type to your document library.
If you are in the Document Set Settings and you see the same thing as the picture below, it means you still need to add the
Folder Content Type to your Document Library (if you created it at the Site Level, it does not automatically exist at the Document Library level - you have to manually add it). Then, within the Document Set Settings, add the
Folder content type within your
Document Set content type.
Have a read of this post on document sets by the Sharepoint Maven, go to the section titled 'HOW TO SET UP A DOCUMENT SET'. It's a thorough step-by-step guide. Or have a look for an inscrutable Microsoft guide!