Use $in and $gte together - Mongodb

Question

I am developing an order system(type Ifood - from deepweb haha) I have 2 models, one of requests(fields: user information and a subdocument with the products) and another of the products.

When the user finalizes the purchase, I wanted to check if it has the quantity that the user ordered (it may be more than one product), and if it has all the products create the order and assume the value of the product (once it has been purchased). But I’m not getting that check.

Product model:

const ProdutoSchema = new mongoose.Schema({
    img_produto: {
        required: true,
        type: String
    },
    nome_produto: {
        trim: true,
        required: true,
        lowercase: true,
        type: String
    },
    preco_produto: {
        required: true, 
        type: Number
    },
    quantidade_produto: {
        required: true,
        type: Number
    }
}, {
    timestamps: true
})

Model request:

const produtosSchema = new mongoose.Schema({
    id_produto: {
        type: String,
        required: true
    },
    qtd_produto: {
        type: Number,
        required: true
    }  
})

const statusSchema = new mongoose.Schema({
    nome: {
        type: String
    }
}, {
    timestamps: true
})

const PedidoSchema = new mongoose.Schema({
    id_usuario: {
        type: String,
        required: true,
    },
    tipo_envio: {
        type: String,
        required: true
    },
    nome_usuario: {
        type: String,
        required: true,
    },
    endereco: {
        type: String,
        required: true
    },
    complemento: {
        type: String,
        required: true
    },
    telefone: {
        type: String,
        required: true
    },
    produtos: [produtosSchema],
    status: [statusSchema]
}, {
    timestamps: true
})

**The way I’m doing: **

const {token, telefone, nome, complemento, endereco, envio, produtos} = req.body

^^ above - take information and products - ex product: [{"_id": 'idDoProduct', "qtd_product": 2}]

 let productData = {ids: [], qtd_produto: []}
            

produtos.map(item => { 
                    productData.ids.push(item._id)

^^ I place all ids in an array (within the loop)-above ^^

productData.qtd_produto.push(Number(item.qtd_produto))

^^ I place all amounts in array (inside the loop)-above ^^

  })
            

Produto.find({_id:{$in: productData.ids}, quantidade_produto: {$in: {$gte: productData.qtd_produto}}}).then(e => {
                

^^ I check if you have this amount of products - with all( the search only with the ids works, but with the quantity_product field does not work) - above ^^

                          res.json(e) 
                    }).

^^ print the product(s) (s) ^^