SELECT 
  f.feature_id, 
  f.purpose, 
  p.product_id, 
  p.parent_product_id, 
  g.id, 
  g.code 
FROM 
  cscart_product_variation_group_features AS f 
  INNER JOIN cscart_product_variation_groups AS g ON f.group_id = g.id 
  INNER JOIN cscart_product_variation_group_products AS p ON f.group_id = p.group_id 
WHERE 
  p.product_id IN (
    1096, 1129, 1098, 1122, 1095, 1078, 1086, 
    1099, 886, 884, 1055, 1056
  )

Query time 0.00034

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "61.41"
    },
    "nested_loop": [
      {
        "table": {
          "table_name": "p",
          "access_type": "range",
          "possible_keys": [
            "PRIMARY",
            "idx_group_id"
          ],
          "key": "PRIMARY",
          "used_key_parts": [
            "product_id"
          ],
          "key_length": "3",
          "rows_examined_per_scan": 13,
          "rows_produced_per_join": 13,
          "filtered": "100.00",
          "index_condition": "(`cscart`.`p`.`product_id` in (1096,1129,1098,1122,1095,1078,1086,1099,886,884,1055,1056))",
          "cost_info": {
            "read_cost": "27.61",
            "eval_cost": "2.60",
            "prefix_cost": "30.21",
            "data_read_per_join": "208"
          },
          "used_columns": [
            "product_id",
            "parent_product_id",
            "group_id"
          ]
        }
      },
      {
        "table": {
          "table_name": "f",
          "access_type": "ref",
          "possible_keys": [
            "idx_group_id"
          ],
          "key": "idx_group_id",
          "used_key_parts": [
            "group_id"
          ],
          "key_length": "3",
          "ref": [
            "cscart.p.group_id"
          ],
          "rows_examined_per_scan": 1,
          "rows_produced_per_join": 13,
          "filtered": "100.00",
          "cost_info": {
            "read_cost": "13.00",
            "eval_cost": "2.60",
            "prefix_cost": "45.81",
            "data_read_per_join": "1K"
          },
          "used_columns": [
            "feature_id",
            "purpose",
            "group_id"
          ]
        }
      },
      {
        "table": {
          "table_name": "g",
          "access_type": "eq_ref",
          "possible_keys": [
            "PRIMARY"
          ],
          "key": "PRIMARY",
          "used_key_parts": [
            "id"
          ],
          "key_length": "3",
          "ref": [
            "cscart.p.group_id"
          ],
          "rows_examined_per_scan": 1,
          "rows_produced_per_join": 13,
          "filtered": "100.00",
          "cost_info": {
            "read_cost": "13.00",
            "eval_cost": "2.60",
            "prefix_cost": "61.41",
            "data_read_per_join": "5K"
          },
          "used_columns": [
            "id",
            "code"
          ]
        }
      }
    ]
  }
}