### 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_
headers[ACL_ORIGIN] = (
            request_headers["origin"]
            if request_headers.get("origin") and not config.DISABLE_CORS_CHECKS
            else "*"
        )
    if ACL_METHODS not in headers:
        headers[ACL_METHODS] = ",".join(CORS_ALLOWED_METHODS)
    if ACL_ALLOW_HEADERS not in headers:
        requested_headers = headers.get(ACL_REQUEST_HEADERS, "")
        requested_headers = re.split(r"[,\s]+", requested_headers) + CORS_ALLOWED_HEADERS
        headers[ACL_ALLOW_HEADERS] = ",".join([h for h in requested_headers if h])
    if ACL_EXPOSE_HEADERS not in headers:
        headers[ACL_EXPOSE_HEADERS] = ",".join(CORS_EXPOSE_HEADERS)
    for header in ALLOWED_CORS_RESPONSE_HEADERS:
        if headers.get(header) == "":
            del headers[header]
def http_exception_to_response(e: HTTPException):
    """Convert a werkzeug HTTP exception to a requests.Response object"""
    response = Response()
    response.status_code = e.code
    response.headers.update(dict(e.get_headers()))
    body = e.get_body()
    response.headers["Content-Length"] = str(len(str(body or "")))
    response._content = body
    return response
def cors_error_response():
    response = Response()
    response.status_code = 403
    return response
def _is_in_allowed_origins(allowed_origins, origin):