the move the documents to hard disk is not just copy and paste, you tell windows to move the folder to the new direction, so all contents new and old are pointed there
the game libraries you can tell them where exactly you want them, steam, origon, ubisoft and spic all of them let you tell where to go, search for games and where to install them
steam in particular allows you to create multiple libraries, i created 2, one in the nvme with gta v, the rest of games on the hard disk, i havent tried with epic and ubisoft yet