How to regoup in subdocuments, multi document that have a same field in MongoDB?

I have a collection in mongoDB that looks like this :

db.mycollection.find({}) 

{
    "_id" : ObjectId("5deb4ce4bbe1b67e6e5611e4"),
    "site" : "MDC",
    "label" : "407",
    "status" : "removed"
}

{
    "_id" : ObjectId("5def36379ca17632de773d7e"),
    "site" : "MDC",
    "label" : "407",
    "status" : "new"
}

{
    "_id" : ObjectId("5df4740eab0d76657c19a7d2"),
    "site" : "MDC",
    "label" : "408",
    "status" : "new"
}

I would like to regroup my documents that have the same value for the field "label" in one document with subdocument of the status, to have something like this :

{
    "_id" : ObjectId("5deb4ce4bbe1b67e6e5611e4"),
    "site" : "MDC",
    "label" : "407",
    "status" : [ 
    {
        "label" : "new"
    }, 
    {
        "label" : "removed"
    }
]
}

I tried different ways (aggregate, update,..) to do this but it's a complete fail...

You need to $group by label or site in order to $push your statuses:

db.collection.aggregate([
    {
        $group: {
            _id: "$label",
            old_id: { $first: "$_id" },
            site: { $first: "$site" },
            status: { $push: { label: "$status" } }
        }
    },
    {
        $project: {
            _id: "$old_id",
            site: 1,
            label: "$_id",
            status: 1
        }
    }
])

Mongo Playground