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' 
    AND cscart_discussion.company_id = 1
  ) 
WHERE 
  dp.status = 'A' 
  and p.product_id in (
    413, 1970, 1937, 433, 414, 407, 402, 1972, 
    388, 1974, 442, 1956, 1936, 416, 326, 
    441, 1957
  ) 
GROUP BY 
  p.product_id

Query time 0.00092

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "37.50"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "0.52"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "ALL",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "rows_examined_per_scan": 104,
            "rows_produced_per_join": 10,
            "filtered": "10.00",
            "cost_info": {
              "read_cost": "21.80",
              "eval_cost": "2.08",
              "prefix_cost": "23.88",
              "data_read_per_join": "4K"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`eshopuga_upgr_4122`.`dp`.`status` = 'A')"
          }
        },
        {
          "table": {
            "table_name": "cscart_discussion",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "object_id",
              "company_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "thread_id"
            ],
            "key_length": "3",
            "ref": [
              "eshopuga_upgr_4122.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "10.40",
              "eval_cost": "0.10",
              "prefix_cost": "36.36",
              "data_read_per_join": "12"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type",
              "company_id"
            ],
            "attached_condition": "((`eshopuga_upgr_4122`.`cscart_discussion`.`company_id` = 1) and (`eshopuga_upgr_4122`.`cscart_discussion`.`object_id` in (413,1970,1937,433,414,407,402,1972,388,1974,442,1956,1936,416,326,441,1957)) and (`eshopuga_upgr_4122`.`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": [
              "eshopuga_upgr_4122.cscart_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.52",
              "eval_cost": "0.10",
              "prefix_cost": "36.98",
              "data_read_per_join": "3K"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}