### 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
path_params=path_params,
                query_string_params=query_string_params,
                method=method,
                resource_path=resource_path,
                request_context=invocation_context.context,
                stage_variables=invocation_context.stage_variables,
            )
            if isinstance(result, FlaskResponse):
                response = flask_to_requests_response(result)
            elif isinstance(result, Response):
                response = result
            else:
                response = LambdaResponse()
                parsed_result = (
                    result if isinstance(result, dict) else json.loads(str(result or "{}"))
                )
                parsed_result = common.json_safe(parsed_result)
                parsed_result = {} if parsed_result is None else parsed_result
                response.status_code = int(parsed_result.get("statusCode", 200))
                parsed_headers = parsed_result.get("headers", {})
                if parsed_headers is not None:
                    response.headers.update(parsed_headers)
                try:
                    result_body = parsed_result.get("body")
                    if isinstance(result_body, dict):
                        response._content = json.dumps(result_body)
                    else:
                        body_bytes = to_bytes(to_str(result_body or ""))
                        if parsed_result.get("isBase64Encoded", False):
                            body_bytes = base64.b64decode(body_bytes)