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 (
    276588, 276589, 276590, 276591, 276592, 
    276593, 276594, 276595, 276596, 276597, 
    276598, 276599, 276600, 276601, 276602, 
    276603, 276604, 276605, 276606, 276607, 
    276608, 276609, 276610, 276611, 276612, 
    276613, 276614, 276615, 276616, 276617
  ) 
GROUP BY 
  p.product_id

Query time 0.00111

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "1.70"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": false,
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "ALL",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "rows_examined_per_scan": 8,
            "rows_produced_per_join": 1,
            "filtered": "12.50",
            "cost_info": {
              "read_cost": "1.22",
              "eval_cost": "0.10",
              "prefix_cost": "1.32",
              "data_read_per_join": "448"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`s2cart`.`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": [
              "s2cart.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "0.25",
              "eval_cost": "0.01",
              "prefix_cost": "1.67",
              "data_read_per_join": "1"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`s2cart`.`cscart_discussion`.`object_id` in (276588,276589,276590,276591,276592,276593,276594,276595,276596,276597,276598,276599,276600,276601,276602,276603,276604,276605,276606,276607,276608,276609,276610,276611,276612,276613,276614,276615,276616,276617)) and (`s2cart`.`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": [
              "s2cart.cscart_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.02",
              "eval_cost": "0.01",
              "prefix_cost": "1.70",
              "data_read_per_join": "393"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}