As you can see, these files/directories are either owned by root:root, or by unknown:users.
Who has created those files (with who I do of course not mean any human person, but which user on which system).
I also assume that you mounting it at /home/user/NAS-Server means that the user “user” (this is a confusing name for a user in a discussion like this :() is NOT the owner of these files.
When I then may also assume that user name “user” has the uid 1000 (but that nmay be differenmt depending on how many users you configured on the system), the you better see that the files on the server are also oened by user: users (that is then 1000:100).
This is the normal Unix/Linux protection against other users. And with NFS you better see that user/group administration on both server and client(s) are the same.