### 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_
get_cors_response,
    make_error_response,
)
from localstack.services.apigateway.integration import (
    LambdaIntegration,
    LambdaProxyIntegration,
    MockIntegration,
    SnsIntegration,
    StepFunctionIntegration,
)
from localstack.services.apigateway.templates import (
    RequestTemplates,
    ResponseTemplates,
    VtlTemplate,
)
from localstack.services.kinesis import kinesis_listener
from localstack.utils import common
from localstack.utils.aws import aws_stack
from localstack.utils.aws.aws_responses import request_response_stream, requests_response
from localstack.utils.http import add_query_params_to_url
LOG = logging.getLogger(__name__)
TARGET_REGEX_PATH_S3_URI = (
    r"^arn:aws:apigateway:[a-zA-Z0-9\-]+:s3:path/(?P<bucket>[^/]+)/(?P<object>.+)$"
)
TARGET_REGEX_ACTION_S3_URI = r"^arn:aws:apigateway:[a-zA-Z0-9\-]+:s3:action/(?:GetObject&Bucket\=(?P<bucket>[^&]+)&Key\=(?P<object>.+))$"
class AuthorizationError(Exception):
    pass
class RequestValidator:
    __slots__ = ["context", "apigateway_client"]
    def __init__(self, context: ApiInvocationContext, apigateway_client):