Notes API: Response is missing `project_id`

GitLab allows supports an API call to search globally for notes: https://docs.gitlab.com/ee/api/search.html#scope-notes However, the returning JSON response is missing project id. Thus it is not possible to associate the search result to any project:

When performing the API call like the following:

curl --header "PRIVATE-TOKEN: <your_access_token>" "https://gitlab.example.com/api/v4/projects/6/search?scope=notes&search=maxime"

it returns JSON as follows:

[
  {
    "id": 191,
    "body": "Harum maxime consequuntur et et deleniti assumenda facilis.",
    "attachment": null,
    "author": {
      "id": 23,
      "name": "User 1",
      "username": "user1",
      "state": "active",
      "avatar_url": "https://www.gravatar.com/avatar/111d68d06e2d317b5a59c2c6c5bad808?s=80&d=identicon",
      "web_url": "http://localhost:3000/user1"
    },
    "created_at": "2017-09-05T08:01:32.068Z",
    "updated_at": "2017-09-05T08:01:32.068Z",
    "system": false,
    "noteable_id": 22,
    "noteable_type": "Issue",
    "noteable_iid": 2
  }
]

As you can see on the response, there is no association from the note to the project. While this response associates to the issue of id 2, it does not tell to which project it associates to.