### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

1. Create kinesis stream with `awslocal kinesis create-stream`
2. Create two firehose delivery stream with `awslocal firehose create-delivery-stream`, both of which have `--kinesis-stream-source-configuration` to the stream created above
3. Put record to the stream
4. Only one of the delivery stream receives the message

### Expected Behavior

At the 4th step, both of the delivery stream should receive the message.
(which was true in real AWS environment.)

### How are you starting LocalStack?

With a `docker run` command

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command, arguments, or `docker-compose.yml`)

    docker run localstack/localstack:2.3.2

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

    docker exec -it admiring_chatelet bash
    (in the localstack container)
    awslocal opensearch create-domain --domain-name my-domain
    awslocal kinesis create-stream --stream-name samplestream --shard-count 2 --region dummy
    awslocal firehose create-delivery-stream --delivery-stream-name s1 --delivery-stream-type KinesisStreamAsSource --kinesis-stream-source-configuration "KinesisStreamARN=arn:aws:kinesis:us-east-1:000000000000:stream/samplestream,RoleARN=arn:aws:kinesis:us-east-1:000000000000:role/stream-role" --amazonopensearchservice-destination-configuration "ClusterEndpoint=http://my-domain.us-east-1.opensearch.localhost.localstack.cloud:4566,IndexName=index1,TypeName=_doc,RoleARN=arn:aws:kinesis:us-east-1:000000000000:role/es-role,S3Configuration={RoleARN=arn:aws:iam::000000000000:role/Firehose-Reader-Role,BucketARN=arn:aws:s3:::kinesis-activity-backup-local}"
    awslocal firehose create-delivery-stream --delivery-stream-name s2 --delivery-stream-type KinesisStreamAsSource --kinesis-stream-source-configuration "KinesisStreamARN=arn:aws:kinesis:us-east-1:000000000000:stream/samplestream,RoleARN=arn:aws:kinesis:us-east-1:000000000000:role/stream-role" --amazonopensearchservice-destination-configuration "ClusterEndpoint=http://my-domain.us-east-1.opensearch.localhost.localstack.cloud:4566,IndexName=index2,TypeName=_doc,RoleARN=arn:aws:kinesis:us-east-1:000000000000:role/es-role,S3Configuration={RoleARN=arn:aws:iam::000000000000:role/Firehose-Reader-Role,BucketARN=arn:aws:s3:::kinesis-activity-backup-local}"
    awslocal kinesis put-record --stream-name samplestream --data '{"test":"value"}' --partition-key 1
    curl http://my-domain.us-east-1.opensearch.localhost.localstack.cloud:4566/index1/_search
    curl http://my-domain.us-east-1.opensearch.localhost.localstack.cloud:4566/index2/_search

by the last two `curl`s, only one of the results shows the given data.

### Environment

```markdown
- OS: MacOS 13.2.1
- LocalStack: 2.3.2
```


### Anything else?

_No response_
self,
        db_flavor,
        db_description,
        delivery_stream_name,
        records,
        unprocessed_records,
        region_name,
    ):
        """
        sends Firehose records to an ElasticSearch or Opensearch database
        """
        search_db_index = db_description["IndexName"]
        domain_arn = db_description.get("DomainARN")
        cluster_endpoint = db_description.get("ClusterEndpoint")
        if cluster_endpoint is None:
            cluster_endpoint = get_opensearch_endpoint(domain_arn)
        db_connection = get_search_db_connection(cluster_endpoint, region_name)
        if db_description.get("S3BackupMode") == ElasticsearchS3BackupMode.AllDocuments:
            s3_dest_desc = db_description.get("S3DestinationDescription")
            if s3_dest_desc:
                try:
                    self._put_records_to_s3_bucket(
                        stream_name=delivery_stream_name,
                        records=unprocessed_records,
                        s3_destination_description=s3_dest_desc,
                    )
                except Exception as e:
                    LOG.warning("Unable to backup unprocessed records to S3. Error: %s", e)