SELECT 
  p.product_id, 
  ifnull(
    count(dp.post_id), 
    0
  ) as discussion_amount_posts 
FROM 
  cscart_discussion 
  INNER JOIN cscart_products as p ON (
    cscart_discussion.object_id = p.product_id
  ) 
  INNER JOIN cscart_discussion_posts as dp ON (
    cscart_discussion.thread_id = dp.thread_id 
    AND cscart_discussion.object_type = 'P'
  ) 
WHERE 
  dp.status = 'A' 
  and p.product_id in (
    831, 830, 829, 828, 827, 841, 840, 839, 
    838, 837, 846, 845, 844, 843, 842, 851, 
    850, 849, 848, 847, 853, 852, 858, 857, 
    856, 855, 854, 863, 862, 861, 860, 859, 
    872, 871, 870, 869, 868, 874, 873
  ) 
GROUP BY 
  p.product_id

Query time 0.00065

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "5.58"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "0.11"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "ALL",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "rows_examined_per_scan": 10,
            "rows_produced_per_join": 1,
            "filtered": "10.00",
            "cost_info": {
              "read_cost": "3.94",
              "eval_cost": "0.20",
              "prefix_cost": "4.14",
              "data_read_per_join": "448"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`cscart`.`dp`.`status` = 'A')"
          }
        },
        {
          "table": {
            "table_name": "cscart_discussion",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "object_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "thread_id"
            ],
            "key_length": "3",
            "ref": [
              "cscart.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "10.74",
            "cost_info": {
              "read_cost": "1.00",
              "eval_cost": "0.02",
              "prefix_cost": "5.34",
              "data_read_per_join": "2"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`cscart`.`cscart_discussion`.`object_id` in (831,830,829,828,827,841,840,839,838,837,846,845,844,843,842,851,850,849,848,847,853,852,858,857,856,855,854,863,862,861,860,859,872,871,870,869,868,874,873)) and (`cscart`.`cscart_discussion`.`object_type` = 'P'))"
          }
        },
        {
          "table": {
            "table_name": "p",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "ref": [
              "cscart.cscart_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.11",
              "eval_cost": "0.02",
              "prefix_cost": "5.47",
              "data_read_per_join": "721"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}