MongoDB - Count number of objects where nested array contains each value

I have a collection of documents and I am trying to count how many documents contain each element in an array that is itself a part of a nested document in an array.

Example of documents:

[
{
  "title": "fruit mix 1",
  "fruit_details": [
    {
      "fruit_names": [
        "strawberry",
        "banana"
      ],
      "category": "berries"
    },
    {
      "fruit_names": [
        "strawberry",
        "apple",
        "mango
      ],
      "category": "red",
    }
  ]
},
{
  "title": "fruit mix 2",
  "fruit_details": [
    {
      "fruit_names": [
        "banana",
        "mango"
      ],
      "category": "tropical",
    }
  ]
},
{
  "title": "fruit mix 3",
  "fruit_details": [
    {
      "fruit_names": [
        "banana",
        "lemon"
      ],
      "category": "yellow",
    },
    {
      "fruit_names": [
        "banana"
      ],
      "category": "long",
    },
  ]
},
]

I want an aggregation pipeline that returns:

[
    {
      "_id": "banana",
      "count": 3
    },
    {
      "_id": "mango",
      "count": 2
    },
    {
      "_id": "lemon",
      "count": 1
    },
    {
      "_id": "strawberry",
      "count": 1
    },
    {
      "_id": "apple",
      "count": 1
    },
]

Banana occurs in all 3 top level documents so the count is 3, mango only occurs in 2, etc.

I'm not sure how to accomplish this without double counting elements that appear in multiple sub-documents in the fruit_details array. For example, strawberry appears twice in the fruit mix 1 document but should only be counted once.

So far I have tried using $setUnion and $group to count unique occurrences. The problem with this is $setUnion unions each fruit_names array and not each element in that array. It also doesn't solve the issue with double counting.

db.collection.aggregate([
  {
    $project: {
      fruit: {
        $setUnion: [
          "$fruit_details.fruit_names",
        ],
      },
    },
  },
  {
    $unwind: "$fruit",
  },
  {
    $group: {
      _id: "$fruit",
      count: {
        $sum: 1,
      },
    },
  },
  {
    $sort: {
      _id: 1,
    },
  },
])

I think the key here, at least for one approach, is to use the $reduce operator. If we modify your initial pipeline stage to look like this:

  {
    $project: {
      fruit: {
        "$reduce": {
          "input": "$fruit_details",
          "initialValue": [],
          "in": {
            "$setUnion": [
              "$$value",
              "$$this.fruit_names",
              
            ]
          }
        }
      }
    }
  },

Then it produces your desired output. Playground demonstration here.

(I also changed the $sort so that the output matched what you were requesting.)