[BUG] Remove ingest processor doesn't handle ignore_missing parameter correctly

[gaobinlong]

Describe the bug
Same to #9687, by checking all of the ingest processors which support template snippets for the field parameter and have ignore_missing parameter, I found that remove ingest processor also has the same problem with rename ingest processor, when setting field to a template snippet {{field_a}} and set ignore_missing to true, if field_a doesn't exist then remove processor throws illegal_argument_exception rather than exiting quietly.

Only remove and rename processor have that problem, other processors work well.

To Reproduce
Steps to reproduce the behavior:
Request:

POST /_ingest/pipeline/_simulate
{
  "pipeline": {
    "description": "_description",
    "processors": [
      {
        "remove": {
          "field": "{{key_xxxx}}",
          "ignore_missing": true
        }
      }
    ]
  },
  "docs": [
    {
      "_index": "index",
      "_id": "id",
      "_source": {
        "key":"foo",
        "foo": "bar=x",
        "target_field":"zoo"
      }
    },
    {
      "_index": "index",
      "_id": "id",
      "_source": {
        "key":"foo",
        "foo": "rab=x",
        "target_field":"zoo"
      }
    }
  ]
}

Response:

{
  "docs": [
    {
      "error": {
        "root_cause": [
          {
            "type": "illegal_argument_exception",
            "reason": "path cannot be null nor empty"
          }
        ],
        "type": "illegal_argument_exception",
        "reason": "path cannot be null nor empty"
      }
    },
    {
      "error": {
        "root_cause": [
          {
            "type": "illegal_argument_exception",
            "reason": "path cannot be null nor empty"
          }
        ],
        "type": "illegal_argument_exception",
        "reason": "path cannot be null nor empty"
      }
    }
  ]
}

Expected behavior
Remove ingest processor can handle ignore_missing parameter correctly, when the resolved template snippet of the field parameter is empty and ignore_missing is true, the processor exits quietly and do nothing.

Host/Environment (please complete the following information):

• OS: [MacOS]
• Version [OpenSearch 2.9]

[gaobinlong]

Closed by #10089.