### 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_
import os
import localstack_client.config
import localstack
VERSION = localstack.__version__
REGION_LOCAL = "local"
ENV_DEV = "dev"
HEADER_LOCALSTACK_EDGE_URL = "x-localstack-edge"
HEADER_LOCALSTACK_REQUEST_URL = "x-localstack-request-url"
HEADER_LOCALSTACK_AUTHORIZATION = "x-localstack-authorization"
HEADER_LOCALSTACK_TARGET = "x-localstack-target"
HEADER_AMZN_ERROR_TYPE = "X-Amzn-Errortype"
DEFAULT_PORT_EDGE = 4566
LOCALHOST = "localhost"
LOCALHOST_IP = "127.0.0.1"
LOCALHOST_HOSTNAME = "localhost.localstack.cloud"
LOCALSTACK_MAVEN_VERSION = "0.2.21"
MAVEN_REPO_URL = "https://repo1.maven.org/maven2"
DEFAULT_SERVICE_PORTS = localstack_client.config.get_service_ports()
BIND_HOST = "0.0.0.0"
DEFAULT_AWS_ACCOUNT_ID = "000000000000"