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 (
    2822, 2244, 2245, 2808, 2351, 2352, 2342, 
    2270, 2843, 2225, 2323, 2266, 13822, 
    2813, 2814, 13821, 4378, 2550, 2551, 
    13142, 15143, 15144, 12684, 14457, 
    2176, 2171, 2169, 2168, 2167, 2165
  ) 
GROUP BY 
  p.product_id

Query time 0.00068

JSON explain

{
  "query_block": {
    "select_id": 1,
    "filesort": {
      "sort_key": "p.product_id",
      "temporary_table": {
        "table": {
          "table_name": "dp",
          "access_type": "ALL",
          "possible_keys": ["thread_id", "thread_id_2"],
          "rows": 8,
          "filtered": 100,
          "attached_condition": "dp.`status` = 'A'"
        },
        "table": {
          "table_name": "cscart_discussion",
          "access_type": "eq_ref",
          "possible_keys": ["PRIMARY", "object_id"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["thread_id"],
          "ref": ["ymonline_livedata.dp.thread_id"],
          "rows": 1,
          "filtered": 100,
          "attached_condition": "cscart_discussion.object_type = 'P'"
        },
        "table": {
          "table_name": "p",
          "access_type": "eq_ref",
          "possible_keys": ["PRIMARY"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["product_id"],
          "ref": ["ymonline_livedata.cscart_discussion.object_id"],
          "rows": 1,
          "filtered": 100,
          "attached_condition": "p.product_id in (2822,2244,2245,2808,2351,2352,2342,2270,2843,2225,2323,2266,13822,2813,2814,13821,4378,2550,2551,13142,15143,15144,12684,14457,2176,2171,2169,2168,2167,2165)",
          "using_index": true
        }
      }
    }
  }
}