I'm part of the "Team Digitale" at a high school and we’ve encountered the same issue after the deprecation of ContactsApp.

I just read the discussion in the link you shared (issuetracker.google.com/issues/199768096). Using GAM7, I wrote this to move (not copy) otherContact to My Contacts, and it seems to work. After that, you can delete it with People.deleteContact().

function move_to_my_contact(contact) {
  var new_rn = contact.resourceName.replace("otherContacts", "people"); 
  People.People.updateContact({
    "resourceName": new_rn, 
    "etag": contact.etag, 
    "memberships": [
      {
        "contactGroupMembership": {
          "contactGroupResourceName": "contactGroups/myContacts"
        }
      }
    ]
  },
  new_rn,
  { updatePersonFields: "memberships" });
}

Did you manage to solve the issue on your own? If so, could you let me know if you found a better solution?

Thank you!