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 (
    371843, 377765, 377766, 377767, 371848, 
    377768, 377769, 377770, 377771, 371861, 
    377772, 377773, 377774, 377775, 371868, 
    377776, 371873, 377777, 377778, 377779, 
    371878, 377780, 377781, 377782, 377783, 
    371884, 377784, 377785, 377786, 371890, 
    377787, 377788, 371895, 377789, 371898, 
    377790, 377791, 371902, 377792, 377793, 
    371905, 377794, 377795, 371912, 377798, 
    377799, 377800, 377801, 371917, 377802, 
    377803, 377735, 377804, 377805, 377806, 
    377807, 377755, 377808, 377809, 377810, 
    371936, 379177, 379178, 379179, 371945, 
    379703, 371984, 379707, 379708, 379709, 
    372021, 379711, 379712, 379713, 379714
  ) 
GROUP BY 
  p.product_id

Query time 0.00072

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "7.29"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "0.10"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "index",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "key": "thread_id_2",
            "used_key_parts": [
              "thread_id",
              "status"
            ],
            "key_length": "6",
            "rows_examined_per_scan": 19,
            "rows_produced_per_join": 1,
            "filtered": "10.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "4.42",
              "eval_cost": "0.38",
              "prefix_cost": "4.80",
              "data_read_per_join": "851"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`webmarco`.`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": [
              "webmarco.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "1.90",
              "eval_cost": "0.02",
              "prefix_cost": "7.08",
              "data_read_per_join": "2"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`webmarco`.`cscart_discussion`.`object_id` in (371843,377765,377766,377767,371848,377768,377769,377770,377771,371861,377772,377773,377774,377775,371868,377776,371873,377777,377778,377779,371878,377780,377781,377782,377783,371884,377784,377785,377786,371890,377787,377788,371895,377789,371898,377790,377791,371902,377792,377793,371905,377794,377795,371912,377798,377799,377800,377801,371917,377802,377803,377735,377804,377805,377806,377807,377755,377808,377809,377810,371936,379177,379178,379179,371945,379703,371984,379707,379708,379709,372021,379711,379712,379713,379714)) and (`webmarco`.`cscart_discussion`.`object_type` = 'P'))"
          }
        },
        {
          "table": {
            "table_name": "p",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "age_verification",
              "status",
              "idx_parent_product_id",
              "idx_master_product_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "ref": [
              "webmarco.cscart_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.10",
              "eval_cost": "0.02",
              "prefix_cost": "7.19",
              "data_read_per_join": "760"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}