How to and a new field and update value dynamically through mongo shell

Is this what are you looking for? as per my prediction.

Input:

[
  {
    "attributes": [
      {
        "basicDetails": [
          {
            "name": "Name",
            "fieldType": "textField",
            "fieldKey": "nameField",
            "fieldDependendent": "",
            "valueString": "",
            "valueArray": "",
            "valueBoolean": false
          },
          {
            "name": "Address",
            "fieldType": "textareaAddressField",
            "fieldKey": "addressField",
            "fieldDependendent": "",
            "valueString": "this address",
            "valueArray": "Test",
            "valueBoolean": false
          }
        ],
        "specificationDetails": "",
        "additionalDetails": ""
      }
    ],
    "status": "",
    "createdAt": "",
    "updatedAt": ""
  }
]

Query:

db.businesslistings.updateMany({},
[
  {
    $set: {
      address: {
        $arrayElemAt: [
          { $arrayElemAt: ["$attributes.basicDetails.valueString", 0] },
          1
        ]
      }
    }
  }
])

Updated Doc:

[
  {
    "address": "this address",
     // other properties ...
   }
]

Playground