curl --request POST \
  --url http://localhost:3000/v1/scheduling/deputy/push-all

{
  "success": true,
  "staff_results": [
    null
  ],
  "unit_updates": [
    null
  ],
  "errors": [
    {
      "error": "<string>",
      "deputyId": 123,
      "name": "<string>",
      "email": "<string>"
    }
  ],
  "summary": {
    "staff_processed": 123,
    "units_updated": 123,
    "errors": 123
  },
  "error": "<string>"
}