Can I restrict other users from storing external files?

Yes, the External files in the media library plugin comes with a wealth of permissions. You can find these in your WordPress backend under Settings > External files in the media library > Permissions. They are assigned on the basis of user roles as used by WordPress. However, you can also deny general access to individual users.

For example, you can set that only administrators have access to the plugin's functions. You can also enable access for all roles, but only allow the use of FTPFTP File Transfer Protocol for all.