MongoDB - Add aggregate field in pipeline depending on all elements of an array

Given the following documents in a collection:

[{
  "_id": {
    "$oid": "63f06283b80a395adf27780d"
  },
  "suppliers": [
    {
      "name": "S1",
      "duesPaid": true
    },
    {
      "name": "S2",
      "duesPaid": true
    }
  ]
},{
  "_id": {
    "$oid": "63f06283b80a395adf27780e"
  },
  "suppliers": [
    {
      "name": "S1",
      "duesPaid": true
    },
    {
      "name": "S2",
      "duesPaid": false
    }
  ]
}]

I would like to create an aggregate field in each document that does the following: If the suppliers array has at least 1 element and every element in that has the duesPaid == true, then add a field to the document suppliersPaid = true. Otherwise, add suppliersPaid = false. The resulting documents from the pipeline should look like this:

[{
  "_id": {
    "$oid": "63f06283b80a395adf27780d"
  },
  "suppliers": [
    {
      "name": "S1",
      "duesPaid": true
    },
    {
      "name": "S2",
      "duesPaid": true
    }
  ],
  "suppliersPaid": true,
},{
  "_id": {
    "$oid": "63f06283b80a395adf27780e"
  },
  "suppliers": [
    {
      "name": "S1",
      "duesPaid": true
    },
    {
      "name": "S2",
      "duesPaid": false
    }
  ],
  "suppliersPaid": false,
}]

I have tried the following pipeline:

[{$addFields: {
  suppliersPaid: {
    $and: [
      { $gte: [{ $size: "$suppliers" }, 1] },
      {
        suppliers: {
          $not: {
            $elemMatch: { duesPaid: false },
          },
        },
      },
    ],
  },
}}]

and I get the following error:

> Invalid $addFields :: caused by :: Unrecognized expression '$elemMatch'

I've tried to eliminate the reliance on $elemMatch per the docs https://www.mongodb.com/docs/manual/reference/operator/query/elemMatch/#single-query-condition as such:

[{$addFields: {
  suppliersPaid: {
    $and: [
      { $gte: [{ $size: "$suppliers" }, 1] },
      {
        suppliers: {
          $not: {
            duesPaid: false
          },
        },
      },
    ],
  },
}}]

But this yields the incorrect result of setting suppliersPaid to true for both documents, which is incorrect.

Note: I would like to avoid using any sort of JS in this code i.e. no $where operator.

For the second condition:

1. $eq - Compare the result from 1.1 to return an empty array.

   1.1. $filter - Filter the documents from suppliers containing { duesPaid: false }.

db.collection.aggregate([
  {
    $addFields: {
      suppliersPaid: {
        $and: [
          {
            $gte: [
              {
                $size: "$suppliers"
              },
              1
            ]
          },
          {
            $eq: [
              {
                $filter: {
                  input: "$suppliers",
                  cond: {
                    $eq: [
                      "$$this.duesPaid",
                      false
                    ]
                  }
                }
              },
              []
            ]
          }
        ]
      }
    }
  }
])

Demo @ Mongo Playground