### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

Authorization headers being sent to API gateway are received on lambdas as "empty string"

### Expected Behavior

_No response_

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

Run a API Gateway with lambda integration

### Environment

```markdown
- OS:
- LocalStack:
```


### Anything else?

_No response_
return validator["validateRequestBody"]
    @staticmethod
    def should_validate_request(validator):
        return validator.get("validateRequestParameters")
def run_authorizer(invocation_context: ApiInvocationContext, authorizer: Dict):
    
    pass
def authorize_invocation(invocation_context: ApiInvocationContext):
    client = aws_stack.connect_to_service("apigateway")
    authorizers = client.get_authorizers(restApiId=invocation_context.api_id, limit=100).get(
        "items", []
    )
    for authorizer in authorizers:
        run_authorizer(invocation_context, authorizer)
def validate_api_key(api_key: str, stage: str):
    usage_plan_ids = []
    client = aws_stack.connect_to_service("apigateway")
    usage_plans = client.get_usage_plans()
    for item in usage_plans.get("items", []):
        api_stages = item.get("apiStages", [])
        usage_plan_ids.extend(
            item.get("id") for api_stage in api_stages if api_stage.get("stage") == stage
        )
    for usage_plan_id in usage_plan_ids:
        usage_plan_keys = client.get_usage_plan_keys(usagePlanId=usage_plan_id)
        for key in usage_plan_keys.get("items", []):
            if key.get("value") == api_key:
                return True
    return False
def is_api_key_valid(is_api_key_required: bool, headers: Dict[str, str], stage: str):