### 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_
from __future__ import annotations
import copy
import functools
import inspect
import json
import logging
import os
import re
import socket
import ssl
import threading
from asyncio.selector_events import BaseSelectorEventLoop
from collections import defaultdict
from typing import DefaultDict, Dict, List, Match, Optional, Type, TypeVar, Union
from urllib.parse import parse_qs, unquote, urlencode, urlparse
import requests
from flask_cors import CORS
from flask_cors.core import (
    ACL_ALLOW_HEADERS,
    ACL_EXPOSE_HEADERS,
    ACL_METHODS,
    ACL_ORIGIN,
    ACL_REQUEST_HEADERS,
)
from requests.models import Request, Response