Dynamodb scan on array of objects Filter Expression

Question

I want to scan dynamodb using filter on product_id showing in below json of table. Can anybody explain how to do scanning using filter of product_id. Wants to scan dynamodb table data using documentclient. Wants to find all fields which has product_id: something

{
 "mandi_id": 1,
 "product": [
  {
   "updated_price": 24,
   "product_id": 2,
   "last_price": 23
  },
  {
   "updated_price": 24,
   "product_id": 5,
   "last_price": 23
  }
 ],
 "status": "active",
 "createdAt": "2022-04-21T08:23:41.774Z",
 "mandiCloseTime": "4pm",
 "mandi_description": "anaj mandi",
 "mandi_name": "gaziabad anaj mandi",
 "state": "uttar pradesh",
 "city": "gaziabad",
 "main_image_s3": "",
 "mandi_latlong": {
  "lng": 77.48325609999999,
  "lat": 28.680346
 },
 "mandiOpenTime": "10am",
 "updatedAt": "2022-04-21T08:23:41.774Z",
 "address_name": "gavindpuram",
 "landmark_name": "mandi",
 "village": "gaziabad",
 "postal": "201013"
}

I have tried the following set of code but it is returning empty array list

var params = {
                TableName: "dev-agrowave-mandi-management",
                // Select: "ALL_ATTRIBUTES"
                FilterExpression: "contains(#product,:product)",
                  ExpressionAttributeNames: {
                      "#product": "product",
                  },
                  ExpressionAttributeValues: { ":product": {"product_id":parseInt(id)}
                }
              };
          
          
      let lastEvaluatedKey = 'dummy'; // string must not be empty
        const itemsAll = [];
        while (lastEvaluatedKey) {
          const data = await docClient.scan(params).promise();
          itemsAll.push(...data.Items);
          lastEvaluatedKey = data.LastEvaluatedKey;
          if (lastEvaluatedKey) {
            params['ExclusiveStartKey'] = lastEvaluatedKey;
          }
        }
        return {msg:itemsAll,params:params};