### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

We are using the `Authorization` header for routing purposes

```
 "authorization: AWS4-HMAC-SHA256 <...>"
```

https://github.com/localstack/localstack/issues/5770

### Expected Behavior

Use a custom header to avoid causing confusion with backend integrations

### How are you starting LocalStack?

With a `docker run` command

### Steps To Reproduce

Run a custom HTTP integration without authorisation

### Environment

```markdown
- OS: 
- LocalStack:
```


### Anything else?

No
try:
            listener_result = listener.forward_request(
                method=handler_chain_request.method,
                path=handler_chain_request.path,
                data=handler_chain_request.data,
                headers=handler_chain_request.headers,
            )
        except HTTPException as e:
            
            return http_exception_to_response(e)
        if isinstance(listener, MessageModifyingProxyListener):
            if isinstance(listener_result, RoutingRequest):
                
                handler_chain_request.method = (
                    listener_result.method or handler_chain_request.method
                )
                handler_chain_request.path = listener_result.path or handler_chain_request.path
                if listener_result.data is not None:
                    handler_chain_request.data = listener_result.data
                if listener_result.headers is not None:
                    handler_chain_request.headers = listener_result.headers
            continue
        if isinstance(listener_result, Response):
            response = listener_result
            break
        if isinstance(listener_result, LambdaResponse):
            response = listener_result
            break
        if isinstance(listener_result, dict):
            response = Response()