### 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
relative_path_w_query_params = "/%s" % path.lstrip("/").partition("/")[2]
    elif test_invoke_match:
        
        stage = None
        region_name = invocation_context.region_name
        api_id = test_invoke_match.group(1)
        resource_id = test_invoke_match.group(2)
        query_string = test_invoke_match.group(4) or ""
        apigateway = aws_stack.connect_to_service(
            service_name="apigateway", region_name=region_name
        )
        resource = apigateway.get_resource(restApiId=api_id, resourceId=resource_id)
        resource_path = resource.get("path")
        relative_path_w_query_params = f"{resource_path}{query_string}"
    else:
        raise Exception(
            f"Unable to extract API Gateway details from request: {path} {dict(headers)}"
        )
    if api_id:
        
        if getattr(THREAD_LOCAL, "request_context", None) is not None:
            THREAD_LOCAL.request_context.headers[MARKER_APIGW_REQUEST_REGION] = API_REGIONS.get(
                api_id, ""
            )
    
    invocation_context.api_id = api_id
    invocation_context.stage = stage
    invocation_context.path_with_query_string = relative_path_w_query_params
    return invocation_context
def extract_api_id_from_hostname_in_url(hostname: str) -> str: