jsonata expression to append the value

Question

i have a json object as in below

{
  "_namespace": "kubernetes",
  "api_paths": [
    {
      "api_action": "post",
      "api_path": "v1/ldap",
      "api_payload": {
        "policies": [
          "reader",
          "writer",
          "encrypt",
          "decrypt"
        ]
      }
    }
  ]
}

i am expecting an outcome like below

{
  "_namespace": "kubernetes",
  "api_paths": [
    {
      "api_action": "post",
      "api_path": "v1/ldap",
      "api_payload": {
        "policies": [
          "reader",
          "writer",
          "encrypt",
          "decrypt",
           "delete"
        ]
      }
    }
  ]
}

can someone help me to correct the expression

$ ~> | {
    "api_paths": $map(function($path) {
        if ($path.api_path["v1/ldap"]) {
            return $merge([$path, {
                "api_payload": $merge([$path.api_payload, {
                    "policies": $append(api_payload.policies, "delete")
                }])
            }])
        } else {
            return $path
        }
    })
}

getting error Expected ":", got "merge"

can someone help me to understand what shall be done to fix this.