### 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_
return "AWS::ApiGateway::UsagePlan"
    def fetch_state(self, stack_name, resources):
        plan_name = self.props.get("UsagePlanName")
        plan_name = self.resolve_refs_recursively(stack_name, plan_name, resources)
        result = aws_stack.connect_to_service("apigateway").get_usage_plans().get("items", [])
        result = [r for r in result if r["name"] == plan_name]
        return (result or [None])[0]
    @staticmethod
    def add_defaults(resource, stack_name: str):
        role_name = resource.get("Properties", {}).get("UsagePlanName")
        if not role_name:
            resource["Properties"]["UsagePlanName"] = generate_default_name(
                stack_name, resource["LogicalResourceId"]
            )
    @staticmethod
    def get_deploy_templates():
        return {
            "create": {
                "function": "create_usage_plan",
                "parameters": {
                    "name": "UsagePlanName",
                    "description": "Description",
                    "apiStages": lambda_keys_to_lower("ApiStages"),
                    "quota": lambda_keys_to_lower("Quota"),
                    "throttle": lambda_keys_to_lower("Throttle"),
                    "tags": params_list_to_dict("Tags"),
                },
            }
        }
    def get_physical_resource_id(self, attribute=None, **kwargs):