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 (
    4003, 4002, 4006, 4001, 4000, 4598, 2510, 
    2507, 2508, 2511, 2509, 3753, 489, 494, 
    488, 492, 416, 497, 495, 3182, 3181, 
    3656, 1610, 1606, 1608, 491, 1609, 1676, 
    1675, 1607, 1677, 1737, 1736, 100, 95, 
    6430, 6431, 7254, 7255, 4050, 4051, 
    4602, 4049, 4034, 4048, 4419, 4601, 
    4422
  ) 
GROUP BY 
  p.product_id

Query time 0.00056

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "5.24"
    },
    "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": 34,
            "rows_produced_per_join": 3,
            "filtered": "10.00",
            "cost_info": {
              "read_cost": "3.65",
              "eval_cost": "0.34",
              "prefix_cost": "3.99",
              "data_read_per_join": "1K"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`dbggbern`.`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": [
              "dbggbern.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "0.85",
              "eval_cost": "0.02",
              "prefix_cost": "5.18",
              "data_read_per_join": "4"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`dbggbern`.`cscart_discussion`.`object_id` in (4003,4002,4006,4001,4000,4598,2510,2507,2508,2511,2509,3753,489,494,488,492,416,497,495,3182,3181,3656,1610,1606,1608,491,1609,1676,1675,1607,1677,1737,1736,100,95,6430,6431,7254,7255,4050,4051,4602,4049,4034,4048,4419,4601,4422)) and (`dbggbern`.`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": [
              "dbggbern.cscart_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.04",
              "eval_cost": "0.02",
              "prefix_cost": "5.24",
              "data_read_per_join": "888"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}