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 (
    12731, 12725, 12727, 12724, 10923, 10920, 
    10922, 12730, 10918, 10916, 10919, 
    10833, 10837, 10835, 10836, 10834, 
    10819, 10827, 10829, 10830, 10832, 
    10828, 12726, 12732, 12598, 12599, 
    12601, 12603, 12600, 12602
  ) 
GROUP BY 
  p.product_id

Query time 0.00058

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 (12731,12725,12727,12724,10923,10920,10922,12730,10918,10916,10919,10833,10837,10835,10836,10834,10819,10827,10829,10830,10832,10828,12726,12732,12598,12599,12601,12603,12600,12602)",
          "using_index": true
        }
      }
    }
  }
}