Set ingest processor can copy the whole object from one field to another

[gaobinlong]

Is your feature request related to a problem? Please describe.
Currently, the set ingest processor cannot copy the whole object from one field to another, the copied result is just string, which is not practical, the use case is that I want to copy a subField of one field to another root level field, and then delete the original field or overwrite it, but I cannot do it by set processor. See the following cases:

Case 1:

Request:

POST _ingest/pipeline/_simulate
{
  "pipeline" : {
    "description": "test",
    "processors": [
        {
          "set": {
            "field": "message",
            "value": "{{message.content}}"
          }
        }
    ]
  },
  "docs" : [
    {
            "_routing":123,
            "_id":1,
            "_source" : {
                "message":{
                  "content":{
                    "foo":1,
                    "bar":"2"
                  }
                }
            }
        }
  ]
}

Response:

{
  "docs": [
    {
      "doc": {
        "_index": "_index",
        "_id": "1",
        "_routing": "123",
        "_source": {
          "message": "{bar=2, foo=1}"
        },
        "_ingest": {
          "timestamp": "2023-09-20T05:47:51.936148084Z"
        }
      }
    }
  ]
}

Case 2

Request:

POST _ingest/pipeline/_simulate
{
  "pipeline" : {
    "description": "test",
    "processors": [
        {
          "set": {
            "field": "content",
            "value": "{{message.content}}"
          }
        },
        {
          "remove": {
            "field": "message"
          }
        }
    ]
  },
  "docs" : [
    {
            "_routing":123,
            "_id":1,
            "_source" : {
                "message":{
                  "content":{
                    "foo":1,
                    "bar":"2"
                  }
                }
            }
        }
  ]
}

Response:

{
  "docs": [
    {
      "doc": {
        "_index": "_index",
        "_id": "1",
        "_routing": "123",
        "_source": {
          "content": "{bar=2, foo=1}"
        },
        "_ingest": {
          "timestamp": "2023-09-20T05:50:03.367657089Z"
        }
      }
    }
  ]
}

The copied result is just string, not an object.

Describe the solution you'd like
Add some enhancement to make set processor can copy the whole object from one field to another, no matter what the data type is, like json object, array, integer, float, all of these types can be copied and keep the same.

Describe alternatives you've considered
Use script processor to do that but it's not easy to use.

[gaobinlong]

Closed by #11870.