### 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:
        response = invoke_rest_api_integration_backend(invocation_context)
        
        
        invocation_context.response = response
        response = apply_response_parameters(invocation_context)
        return response
    except Exception as e:
        msg = f"Error invoking integration for API Gateway ID '{invocation_context.api_id}': {e}"
        LOG.exception(msg)
        return make_error_response(msg, 400)
def invoke_rest_api_integration_backend(invocation_context: ApiInvocationContext):
    
    invocation_path = invocation_context.path_with_query_string
    method = invocation_context.method
    data = invocation_context.data
    headers = invocation_context.headers
    api_id = invocation_context.api_id
    stage = invocation_context.stage
    resource_path = invocation_context.resource_path
    response_templates = invocation_context.response_templates
    integration = invocation_context.integration
    
    relative_path, query_string_params = extract_query_string_params(path=invocation_path)