[BUG] Bulk upsert does not behave like a single Upsert, with an ingestion pipeline

Describe the bug A single Upsert works as expected with an ingestion pipeline. But the same operation in a Bulk upsert doesn't give the same result.

To Reproduce Steps to reproduce the behavior:

1. Create an ingestion pipeline that aims to calculate a duration between 2 dates

PUT _ingest/pipeline/pipeline-duration
{
  "description": "This pipeline complete data with begin, end and duration",
  "processors": [
    {
      "script": {
        "description": "Old duration",
        "lang": "painless",
        "source": "ctx.old_duration = 'Old duration was : '+ctx.event_duration;"
      }
    },
    {
      "script": {
        "description": "Begin computation",
        "lang": "painless",
        "params": { "_source": "" }, 
        "source": """
          if (ctx.event_begin == null || ((long) ctx.event_min) < ((long) ctx.event_begin)) { 
            ctx.event_begin = (long)ctx.event_min; 
          } else { 
            ctx.event_min = ctx.event_begin 
          } 
        """
      }
    },
    {
      "script": {
        "description": "End computation",
        "lang": "painless",
        "params": { "_source": "" }, 
        "source": """
          if (ctx.event_end == null || ((long) ctx.event_max) > ((long) ctx.event_end)) { 
            ctx.event_end = (long)ctx.event_max; 
          } else { 
            ctx.event_max = ctx.event_end 
          } 
        """
      }
    },
    {
      "script": {
        "description": "Duration computation",
        "lang": "painless",
        "source": "ctx.event_duration = (long)(ctx['event_max']-ctx['event_min']);"
      }
    }
  ]
}

2. Create an index with the ingest pipeline

PUT index-duration
{
  "aliases": {},
  "mappings": {
    "properties": {
      "event_min": {
        "type": "float"
      },
      "event_max": {
        "type": "float"
      },
      "event_begin": {
        "type": "date",
        "format": "epoch_millis"
      },
      "event_end": {
        "type": "date",
        "format": "epoch_millis"
      },
      "event_duration": {
        "type": "long"
      },
      "event_name": {
        "type": "keyword"
      },
      "old_duration": {
        "type": "keyword"
      }
    }
  },
  "settings": {
    "index": {
      "final_pipeline": "pipeline-duration"
    }
  }
}

3. Execute the 2 following Update operations :

POST index-duration/_update/doc_duration
{
  "doc" : {
    "event_min": 1,
    "event_max": 2,
	"event_name": "occurrence_1"
  },
  "doc_as_upsert": true
} 

second time

POST index-duration/_update/doc_duration
{
  "doc" : {
    "event_min": 3,
    "event_max": 5,
    "event_name": "occurrence_2"
  },
  "doc_as_upsert": true
} 

then check the document GET index-duration/_doc/doc_duration it gives :

  "_source": {
    "event_end": 5,
    "old_duration": "Old duration was : 1",
    "event_duration": 4,
    "event_min": 1,
    "event_name": "occurrence_2",
    "event_max": 5,
    "event_begin": 1
  }

4. Now execute the same Update operations but embedded in a bulk

POST _bulk
{ "update": { "_index": "index-duration", "_id": "doc_duration_issue" } }
{ "doc" : { "event_min": 1, "event_max": 2, "event_name": "occurrence_1"},"doc_as_upsert": true} 

second time :

POST _bulk
{ "update": { "_index": "index-duration", "_id": "doc_duration_issue" } }
{ "doc" : { "event_min": 3, "event_max": 5, "event_name": "occurrence_2"},"doc_as_upsert": true} 

Then check the document with GET index-duration/_doc/doc_duration_issue it gives :

  "_source": {
    "event_end": 5,
    "old_duration": "Old duration was : null",
    "event_duration": 2,
    "event_min": 3,
    "event_name": "occurrence_2",
    "event_max": 5,
    "event_begin": 3
  }

Expected behavior Bulk Upsert and "Single" Upsert should have the same behavior when there is an ingestion pipeline. We expect to get the same values than doc_duration :

  "_source": {
    "event_end": 5,
    "old_duration": "Old duration was : 1",
    "event_duration": 4,
    "event_min": 1,
    "event_name": "occurrence_2",
    "event_max": 5,
    "event_begin": 1
  }

Plugins odfe-node1 opensearch-alerting 2.11.0.0 odfe-node1 opensearch-anomaly-detection 2.11.0.0 odfe-node1 opensearch-asynchronous-search 2.11.0.0 odfe-node1 opensearch-cross-cluster-replication 2.11.0.0 odfe-node1 opensearch-custom-codecs 2.11.0.0 odfe-node1 opensearch-geospatial 2.11.0.0 odfe-node1 opensearch-index-management 2.11.0.0 odfe-node1 opensearch-job-scheduler 2.11.0.0 odfe-node1 opensearch-knn 2.11.0.0 odfe-node1 opensearch-ml 2.11.0.0 odfe-node1 opensearch-neural-search 2.11.0.0 odfe-node1 opensearch-notifications 2.11.0.0 odfe-node1 opensearch-notifications-core 2.11.0.0 odfe-node1 opensearch-observability 2.11.0.0 odfe-node1 opensearch-performance-analyzer 2.11.0.0 odfe-node1 opensearch-reports-scheduler 2.11.0.0 odfe-node1 opensearch-security 2.11.0.0 odfe-node1 opensearch-security-analytics 2.11.0.0 odfe-node1 opensearch-sql 2.11.0.0

Host/Environment (please complete the following information):

• docker images : opensearchproject/opensearch:2.11.0

Additional context This issue is not exactly the same than the one posted here : #2607 That's why I prefer open a new one.