### 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
payload["input"] = json.dumps(payload["input"])
            
            method_name = (
                camel_to_snake_case(action) if action != "StartSyncExecution" else "start_execution"
            )
            try:
                method = getattr(client, method_name)
            except AttributeError:
                msg = "Invalid step function action: %s" % method_name
                LOG.error(msg)
                return make_error_response(msg, 400)
            result = method(**payload)
            result = json_safe({k: result[k] for k in result if k not in "ResponseMetadata"})
            response = requests_response(
                content=result,
                headers=aws_stack.mock_aws_request_headers(),
            )
            if action == "StartSyncExecution":
                
                result = await_sfn_execution_result(result["executionArn"])
                result_status = result.get("status")
                if result_status != "SUCCEEDED":
                    return make_error_response(
                        "StepFunctions execution %s failed with status '%s'"
                        % (result["executionArn"], result_status),
                        500,
                    )
                result = json_safe(result)
                response = requests_response(content=result)