Mongodb: How to pass another stage inside $group?

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Sample Data

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Expected Output:

[
  {
    "_id": "healty",
    "doc_count": 2,
    "ingredients": {
      "Leaves": {
        "1.2g": 1,
        "1.5g": 1
      },
      "Spinach": {
        "12g": 1,
        "18g": 1
      }
    }
  },
  {
    "_id": "junk",
    "doc_count": 3,
    "ingredients": {
      "cheese": {
        "100g": 1,
        "120g": 2
      },
      "meat": {
        "50g": 1,
        "60g": 1,
        "70g": 1
      }
    }
  }
]

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Aggregation Below: Playground1

db.collection.aggregate([
  {
    $group: {       
      "_id": "$type",  // grouping the document by "type" field
      "ingredients": {
        $push: "$$ROOT"  //want to run Playground2 aggrgtion in each of it
      },
      "doc_count": {
        $sum: 1        // total count
      }
    }
  }
])

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After that,

I’ve also figured out an Another Step to convert the ingredients array after it: Playground2

But, this aggregation is for All the documents. I want to make Playground2 aggregation work for the ingredients field only in each group Object.

It’s similar to combining Playground1 & Playground2. How do I do this?