### 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 json
import logging
import re
from typing import Any, Dict, Union
from urllib.parse import urljoin
import requests
from jsonschema import ValidationError, validate
from requests.models import Response
from localstack import config
from localstack.aws.accounts import get_aws_account_id
from localstack.constants import APPLICATION_JSON, HEADER_LOCALSTACK_AUTHORIZATION
from localstack.services.apigateway import helpers
from localstack.services.apigateway.context import ApiInvocationContext
from localstack.services.apigateway.helpers import (
    extract_path_params,
    extract_query_string_params,