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 (
    262341, 262509, 262398, 262852, 262853, 
    262854, 262855, 262856, 262857, 262858, 
    262859, 262860, 264355, 264357, 262924, 
    264649, 264650, 264651, 262345, 264652, 
    264653, 264654, 265021, 265022, 265023, 
    265024, 265025, 265026, 265053, 265054, 
    265055, 265056, 265057, 265058, 359697, 
    359698, 359699, 359700, 359701, 359702, 
    359703, 359704, 359705, 359706, 359707, 
    359708, 359709, 359710, 359715, 359716, 
    359717, 359718, 359719, 359720, 359721, 
    359722, 359723, 359724, 359725, 359726, 
    359727, 359728, 359729, 359730, 359780, 
    359783, 359784, 359787, 359788, 359791, 
    359792, 359795, 359796, 359799, 388351, 
    388352, 388353, 388354, 388355, 388356
  ) 
GROUP BY 
  p.product_id

Query time 0.00102

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 (262341,262509,262398,262852,262853,262854,262855,262856,262857,262858,262859,262860,264355,264357,262924,264649,264650,264651,262345,264652,264653,264654,265021,265022,265023,265024,265025,265026,265053,265054,265055,265056,265057,265058,359697,359698,359699,359700,359701,359702,359703,359704,359705,359706,359707,359708,359709,359710,359715,359716,359717,359718,359719,359720,359721,359722,359723,359724,359725,359726,359727,359728,359729,359730,359780,359783,359784,359787,359788,359791,359792,359795,359796,359799,388351,388352,388353,388354,388355,388356)) 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"
            ]
          }
        }
      ]
    }
  }
}