How to do double grouping in MongoDB?

Question

MongoDB

Hello. For the first time I deal with MongoDB, a question arose when grouping data.
Given data for two days:

db.test.insert({
    "_id" : ObjectId("13edebb315d8952400407343"),
    "create_at" : ISODate("2012-12-19T12:00:00.000Z"),
    "item" : {
        "tags" : [ 
            "aaaa"
        ],
        "event" : "accepted",
    }
});
    
db.test.insert({
    "_id" : ObjectId("13edebb39e60c73800b35727"),
    "create_at" : ISODate("2012-12-19T12:05:00.000Z"),
    "item" : {
        "tags" : [ 
            "aaaa"
        ],
        "event" : "delivered"
    }
});

db.test.insert({
    "_id" : ObjectId("13edebb315d8952400407344"),
    "create_at" : ISODate("2012-12-19T13:40:00.000Z"),
    "item" : {
        "tags" : [ 
            "bbbb"
        ],
        "event" : "accepted",
    }
});

db.test.insert({
    "_id" : ObjectId("13edebb39e60c73800b35728"),
    "create_at" : ISODate("2012-12-19T13:45:00.000Z"),
    "item" : {
        "tags" : [ 
            "bbbb"
        ],
        "event" : "delivered"
    }
});

db.test.insert({
    "_id" : ObjectId("13edebb315d8952400407345"),
    "create_at" : ISODate("2012-12-20T16:30:00.000Z"),
    "item" : {
        "tags" : [],
        "event" : "accepted",
    }
});

db.test.insert({
    "_id" : ObjectId("13edebb39e60c73800b35729"),
    "create_at" : ISODate("2012-12-20T16:35:00.000Z"),
    "item" : {
        "tags" : [],
        "event" : "delivered"
    }
});

At the output, you need to get the result:

{
  "total_count": 6
  "items": [
    {
      "total_count": 2,
      "created_at": "Wed, 19 Dec 2012 00:00:00 GMT",
      "tags": {
        "aaaa": 1,
        "supporta": 1
      },
      "event": "sent"
    },
    {
      "total_count": 2,
      "created_at": "Wed, 19 Dec 2012 00:00:00 GMT",
      "tags": {
        "aaaa": 1,
        "supporta": 1
      },
      "event": "delivered"
    },
    {
      "total_count": 1,
      "created_at": "Wed, 20 Dec 2012 00:00:00 GMT",
      "tags": {},
      "event": "sent"
    },
    {
      "total_count": 1,
      "created_at": "Wed, 20 Dec 2012 00:00:00 GMT",
      "tags": {},
      "event": "delivered"
    }
}

So far, it has been possible to form part of the necessary data by requesting:

db.test.aggregate([ 
  {$group:      
   {          
     _id:{event:'$item.event', doy:{$dayOfYear:'$create_at'} },
     total_count:{$sum:1},
     created_at:{$first: '$create_at'},
     tags: {$addToSet: '$item.tags'}
   },
  },
  {$project:{total_count:1,  _id:0, event:'$_id.event', created_at:1, tags:1}}
])

But how to get the necessary information about the tags, that is, an array of tags and their number?
And also in the date indicate the beginning of the day 00:00:00?