### 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_
if ":" in (secret_id or ""):
        return secret_id
    pattern = "arn:aws:secretsmanager:%s:%s:secret:%s"
    return _resource_arn(secret_id, pattern, account_id=account_id, region_name=region_name)
def cloudformation_stack_arn(stack_name, stack_id=None, account_id=None, region_name=None):
    stack_id = stack_id or "id-123"
    pattern = "arn:aws:cloudformation:%s:%s:stack/%s/{stack_id}".format(stack_id=stack_id)
    return _resource_arn(stack_name, pattern, account_id=account_id, region_name=region_name)
def cf_change_set_arn(change_set_name, change_set_id=None, account_id=None, region_name=None):
    change_set_id = change_set_id or "id-456"
    pattern = "arn:aws:cloudformation:%s:%s:changeSet/%s/{cs_id}".format(cs_id=change_set_id)
    return _resource_arn(change_set_name, pattern, account_id=account_id, region_name=region_name)
def dynamodb_table_arn(table_name, account_id=None, region_name=None):
    table_name = table_name.split(":table/")[-1]
    pattern = "arn:aws:dynamodb:%s:%s:table/%s"
    return _resource_arn(table_name, pattern, account_id=account_id, region_name=region_name)
def dynamodb_stream_arn(table_name, latest_stream_label, account_id=None):
    account_id = get_account_id(account_id)
    return "arn:aws:dynamodb:%s:%s:table/%s/stream/%s" % (
        get_region(),
        account_id,
        table_name,
        latest_stream_label,
    )
def cloudwatch_alarm_arn(alarm_name, account_id=None, region_name=None):
    pattern = "arn:aws:cloudwatch:%s:%s:alarm:%s"
    return _resource_arn(alarm_name, pattern, account_id=account_id, region_name=region_name)
def log_group_arn(group_name, account_id=None, region_name=None):