### 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_
)
        if extended_s3_destination_update:
            destination["ExtendedS3DestinationDescription"] = convert_extended_s3_update_to_desc(
                extended_s3_destination_update
            )
        if http_endpoint_destination_update:
            destination["HttpEndpointDestinationDescription"] = convert_http_update_to_desc(
                http_endpoint_destination_update
            )
        return UpdateDestinationOutput()
    def _reencode_record(self, record: Record) -> Record:
        """
        The ASF decodes the record's data automatically. But most of the service integrations (kinesis, lambda, http)
        are working with the base64 encoded data.
        """
        if "Data" in record:
            record["Data"] = base64.b64encode(record["Data"])
        return record
    def _reencode_records(self, records: List[Record]) -> List[Record]:
        return [self._reencode_record(r) for r in records]
    def _process_records(
        self,
        account_id: str,
        region_name: str,
        fh_d_stream: str,
        records: List[Record],
    ):
        """Process the given records from the underlying Kinesis stream"""
        return self._put_records(account_id, region_name, fh_d_stream, records)
    def _put_record(