[BUG]Query support on flat_object field with dotted sub field names is unreliable

[ngnwn]

Describe the bug
I have an index with a field of type “flat_object,” and the JSON object for that field contains dotted sub-field names. I’m attempting to apply a term query using the entire key and value but it doesn't work as expected

To Reproduce
Steps to reproduce the behavior:

1. Create an index with mapping:

PUT /my-test-os-index
{
  "mappings": {
    "properties": {
      "transcript": {"type": "flat_object"}
    }
  }
}

2. Index a single document

POST my-test-os-index/_doc
{
  "transcript": {
    "one": "FAILED",
    "two.one": "FAILED",
    "three": "FAILED"
  }
}

3. Run a term query

POST my-test-os-index/_search
{
  "query": {
    "term": {"transcript.three": "FAILED"}
  }
}

4. The results are empty

Expected behavior
We expect the one indexed document to be returned cause it matches the criteria

Plugins
I am using OpenSearch 2.9

Host/Environment (please complete the following information):
Using OS serverless

Additional context

POST my-test-os-index/_search
{
  "query": {
    "term": {"transcript.one": "FAILED"}
  }
}

This query retrieves the document making the results order dependent and unreliable

[peternied]

Thanks for filing this issue