How to move time-machine backups to a new external disk?
It seems you're not using the standard rsync program that comes with macOS, but rather a different version from for example HomeBrew. In that case you'll probably want to use the --acls option to ensure that proper ACLs are being used.

The "operation not permitted" even as root seems to indicate that you're running Catalina, and haven't given the program the necessary permissions. In Catalina there's a seperate security layer that protects the user from malicious programs - even those running as root. You'll want to open System Preferences => Security &amp; Privacy and give "Files and Folders" permissions and/or "Full Disk Access" permissions to the Terminal.app and rsync programs.