### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

I am creating an API Gateway with a Lambda Authorizer via a CloudFormation stack. The stack specifies a data mapping from the request body passed to the API to the request body expected by Kinesis (search `RequestTemplates` in the attached CloudFormation template). It also specifies a model and a validator which are used to validate the request body. Both of these aspects of the API work in AWS itself but appear to be ignored in LocalStack. 

If I test with the same request body I passed to AWS, LocalStack throws an error indicating that the PutRecord call to Kinesis isn't providing a PartitionKey field. The data mapping should've taken care of it. If I then invoke the API in LocalStack with what *should* be sent to Kinesis, the invocation succeeds. This second invocation *should* violate the validation logic in the template, but doesn't. 

### Expected Behavior

The data mapping should correctly map the passed-in request body to a request body which Kinesis can understand. In addition, the validator should reject requests that don't pass validation.

### 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 --rm -it -p 4566:4566 -p 4571:4571 -e LOCALSTACK_API_KEY=$env:LOCALSTACK_API_KEY localstack/localstack

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

```
# create s3 bucket and upload c# lambda authorizer zip to s3
aws --endpoint-url=http://localhost:4566 s3api create-bucket --bucket timeseries-ingest-lambda-artifacts
aws --endpoint-url=http://localhost:4566 s3 cp index.zip s3://timeseries-ingest-lambda-artifacts/KinesisAPILambdaAuthorizer/index.zip
# create stream
aws --endpoint-url=http://localhost:4566 kinesis create-stream --stream-name test-timeseries-ingest-stream --shard-count 1
# create stack
aws --endpoint-url=http://localhost:4566 cloudformation create-stack --stack-name test-kinesis-api --template-body file://cloudformation-kinesis-api-resources-PER-ENVIRONMENT.yaml --parameters ParameterKey=AppName,ParameterValue=timeseries-ingest ParameterKey=Environment,ParameterValue=test
```

This is the CloudFormation template: [cloudformation-kinesis-api-resources-PER-ENVIRONMENT.yaml.txt](https://github.com/localstack/localstack/files/7973188/cloudformation-kinesis-api-resources-PER-ENVIRONMENT.yaml.txt)

### Environment

```markdown
- OS: Ubuntu 20.04
- LocalStack: latest (as of 3 days ago)
```


### Anything else?

_No response_
bucket_name = resource_props.get("BucketName")
            bucket_name = resolve_refs_recursively(stack, bucket_name)
            if attribute == "Arn":
                return aws_stack.s3_bucket_arn(bucket_name)
            return bucket_name
    elif resource_type == "Elasticsearch::Domain":
        if attribute == "DomainEndpoint":
            domain_status = resource_state.get("DomainStatus", {})
            result = domain_status.get("Endpoint")
            if result:
                return result
        if attribute in ["Arn", "DomainArn"]:
            domain_name = resource_props.get("DomainName") or resource_state.get("DomainName")
            return aws_stack.es_domain_arn(domain_name)
    elif resource_type == "StepFunctions::StateMachine":
        if is_ref_attr_or_arn:
            return resource_state["stateMachineArn"]
    elif resource_type == "SNS::Topic":
        if is_ref_attribute and resource_state.get("TopicArn"):
            topic_arn = resource_state.get("TopicArn")
            return resolve_refs_recursively(stack, topic_arn)
    elif resource_type == "SQS::Queue":
        if is_ref_attr_or_arn:
            if attribute == "Arn" and resource_state.get("QueueArn"):
                return resolve_refs_recursively(stack, resource_state.get("QueueArn"))
            return aws_stack.get_sqs_queue_url(resource_props.get("QueueName"))
    attribute_lower = common.first_char_to_lower(attribute)
    result = resource_state.get(attribute) or resource_state.get(attribute_lower)
    if result is None and isinstance(resource, dict):
        result = resource_props.get(attribute) or resource_props.get(attribute_lower)