Use $setWindowFields to group daily users registered by channel

Hi,
I’m trying to use $setWindowFields to group my registered users by mktChannel AND on a daily basis. In addition, I need to count the total number of users registered daily.

Demo data:

[
  {
    "_id": ObjectId("66b016d60e3592d71f966d1a"),
    "dateRegistered": ISODate("2024-08-01T00:03:34.334Z"),
    "name": "user1",
    "mktChannel": "facebook"
  },
  {
    "_id": ObjectId("66b053710e3592d71f9672b5"),
    "dateRegistered": ISODate("2024-08-01T04:22:09.931Z"),
    "name": "user2",
    "mktChannel": "facebook"
  },
  {
    "_id": ObjectId("66b066190e3592d71f9692cd"),
    "dateRegistered": ISODate("2024-08-01T05:41:45.110Z"),
    "name": "user3",
    "mktChannel": "linkedin"
  },
  {
    "_id": ObjectId("66b070df0e3592d71f96a5d9"),
    "dateRegistered": ISODate("2024-08-02T06:27:43.740Z"),
    "name": "user4",
    "mktChannel": "instagram"
  },
  {
    "_id": ObjectId("66b07a520e3592d71f96ba14"),
    "dateRegistered": ISODate("2024-08-02T07:08:02.896Z"),
    "name": "user5",
    "mktChannel": "facebook"
  },
  {
    "_id": ObjectId("66b07c9f0e3592d71f96bb97"),
    "dateRegistered": ISODate("2024-08-02T07:17:51.406Z"),
    "name": "user6",
    "mktChannel": "facebook"
  },
  {
    "_id": ObjectId("66b07d2c0e3592d71f96bcf0"),
    "dateRegistered": ISODate("2024-08-02T07:20:12.944Z"),
    "name": "user7",
    "mktChannel": "facebook"
  },
  {
    "_id": ObjectId("66b081500e3592d71f96c557"),
    "dateRegistered": ISODate("2024-08-03T07:37:52.883Z"),
    "name": "user8",
    "mktChannel": "linkedin"
  },
  {
    "_id": ObjectId("66b084940e3592d71f96ce96"),
    "dateRegistered": ISODate("2024-08-03T07:51:48.830Z"),
    "name": "user9",
    "mktChannel": "none"
  }
]

I want to return something like this:

[
    {
        "day": "2024-08-01",
        "usersRegistered": 3,
        "usersByChannel": [
            {
                "channel": "facebook",
                "count": 2,
                "usersIds": [
                    "66b016d60e3592d71f966d1a",
                    "66b053710e3592d71f9672b5"
                ],
                "usersNames": [
                    "user1",
                    "user2"
                ]
            },
            {
                "channel": "linkedin",
                "count": 1,
                "users": [
                    "66b066190e3592d71f9692cd"
                ],
                "usersNames": [
                    "user3"
                ]
            }
        ]
    },
    {
        "day": "2024-08-02",
        "usersRegistered": 4,
        "usersByChannel": [
            {
                "channel": "instagram",
                "count": 2,
                "users": [
                    "66b070df0e3592d71f96a5d9",
                    "66b07c9f0e3592d71f96bb97"
                ],
                "usersNames": [
                    "user4",
                    "user6"
                ]
            },
            {
                "channel": "email",
                "count": 1,
                "users": [
                    "66b07a520e3592d71f96ba14"
                ],
                "usersNames": [
                    "user5"
                ]
            }
        ]
    },
    {
        "day": "2024-08-03",
        "usersRegistered": 2,
        "usersByChannel": [
            {
                "channel": "linkedin",
                "count": 1,
                "users": [
                    "66b081500e3592d71f96c557"
                ],
                "usersNames": [
                    "user8"
                ]
            },
            {
                "channel": "none",
                "count": 1,
                "users": [
                    "66b084940e3592d71f96ce96"
                ],
                "usersNames": [
                    "user9"
                ]
            }
        ]
    }
]

I knew (more or less) how to achive this result by using multiple $group stages, but I really can’t figure out how to solve this using the (relative) new stage $setWindowFields . Tried using range unit “day” but not obtaing anything useful.

Can someone help me or just show the direction?

DEMO CODE PLAYGROUND HERE: Mongo playground