What I needed to do was to first create a folder inside Godot by rightclicking res:// and choosing "New Folder...", giving it the same name as the folder I want to import. This creates a folder by that name inside the project root folder.
Then I open the folder I want to import in the operating systems file explorer, copy/cutting all the content inside and then open the folder I created in the project root and pasting the content there.
After that, when focusing the Godot Window again, it starts an import operation.