### 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 ..api import RequestContext
from ..chain import Handler, HandlerChain
CORS_ALLOWED_HEADERS = [
    "authorization",
    "cache-control",
    "content-length",
    "content-md5",
    "content-type",
    "etag",
    "location",
    "x-amz-acl",
    "x-amz-content-sha256",
    "x-amz-date",
    "x-amz-request-id",
    "x-amz-security-token",
    "x-amz-tagging",
    "x-amz-target",
    "x-amz-user-agent",
    "x-amz-version-id",
    "x-amzn-requestid",
    "x-localstack-target",
    
    "amz-sdk-invocation-id",
    "amz-sdk-request",
]
if EXTRA_CORS_ALLOWED_HEADERS:
    CORS_ALLOWED_HEADERS += EXTRA_CORS_ALLOWED_HEADERS.split(",")
CORS_ALLOWED_METHODS = ("HEAD", "GET", "PUT", "POST", "DELETE", "OPTIONS", "PATCH")
CORS_EXPOSE_HEADERS = (
    "etag",