### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

Here are the kinesis events from inserting/deleting a dynamodb item:

```
{"eventID":"cf1199b0","eventVersion":"1.1","dynamodb":{"ApproximateCreationDateTime":1.635284406858227E9,"SizeBytes":56,"Keys":{"hash":{"S":"hash-691"},"range":{"S":"range-153"}},"NewImage":{"hash":{"S":"hash-691"},"range":{"S":"range-153"}}},"awsRegion":"us-east-1","eventSource":"aws:dynamodb","eventName":"INSERT","tableName":"bug"}

{"eventID":"976b515b","eventVersion":"1.1","dynamodb":{"ApproximateCreationDateTime":1.6352844070969691E9,"SizeBytes":4,"Keys":{"hash":{"S":"hash-691"},"range":{"S":"range-153"}},"OldImage":null},"awsRegion":"us-east-1","eventSource":"aws:dynamodb","eventName":"REMOVE","tableName":"bug"}
```

Note that the remove event has `OldImage` = `null`

### Expected Behavior

I expected `OldImage` to be `{"hash":{"S":"hash-691"},"range":{"S":"range-153"}}`.

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

https://github.com/achaphiv/issue-localstack-dynamodb-stream-to-kinesis

```
# Create table/stream and hook them up
docker-compose up -d

# Create/delete an item
./mvnw -P write-to-dynamodb

# See the produced records
./mvnw -P watch-kinesis
```

### Environment

```markdown
- OS: Manjaro Linux
- LocalStack: 0.12.19
```


### Anything else?

_No response_
for record in records:
                event_sources_or_streams_enabled = (
                    event_sources_or_streams_enabled
                    or has_event_sources_or_streams_enabled(
                        record["eventSourceARN"], streams_enabled_cache
                    )
                )
        elif action == "PutItem":
            if response.status_code == 200:
                keys = dynamodb_extract_keys(item=data["Item"], table_name=table_name)
                if isinstance(keys, Response):
                    return keys
                
                if response._content == "{}":
                    response._content = update_put_item_response_content(data, response._content)
                    fix_headers_for_updated_response(response)
                if event_sources_or_streams_enabled:
                    existing_item = self._thread_local("existing_item")
                    
                    stream_spec = dynamodb_get_table_stream_specification(table_name=table_name)
                    record["eventName"] = "INSERT" if not existing_item else "MODIFY"
                    
                    record["dynamodb"]["Keys"] = keys
                    record["dynamodb"]["NewImage"] = data["Item"]
                    record["dynamodb"]["SizeBytes"] = len(json.dumps(data["Item"]))
                    record["eventID"] = short_uid()
                    if stream_spec:
                        record["dynamodb"]["StreamViewType"] = stream_spec["StreamViewType"]
                    if existing_item:
                        record["dynamodb"]["OldImage"] = existing_item