If no RCD, then one will need to be fitted. This unfortunately makes this work notifiable as well.
Really? I don't see "adding an RCD" on the list of notifiable activities.
If you change the CU then yes, of course.
Certainly the RCD must be properly tested and the results recorded on the minor works cert for the changes.
Watch out for the addendum to 17th edition. You may find that having an RCD for a minor change like moving a socket will not be necessary in the future.